ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV)

Stability Analysis for a Class of Linear 2x2 Hyperbolic PDEs Using a Backstepping Transform

David Bou Saba, Federico Bribiesca Argomedo, Jean Auriol, Michael Di Loreto and Florent Di Meglio
IEEE Transactions on Automatic Control 1 (2019)
DOI: 10.1109/TAC.2019.2934384
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ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws

Christophe Prieur and Frédéric Mazenc
Mathematics of Control, Signals, and Systems 24 (1-2) 111 (2012)
DOI: 10.1007/s00498-012-0074-2
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On boundary feedback stabilization of non-uniform linear hyperbolic systems over a bounded interval

Georges Bastin and Jean-Michel Coron
Systems & Control Letters 60 (11) 900 (2011)
DOI: 10.1016/j.sysconle.2011.07.008
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Rational Transfer Function Model for a Double-Pipe Parallel-Flow Heat Exchanger

Krzysztof Bartecki
Symmetry 12 (8) 1212 (2020)
DOI: 10.3390/sym12081212
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Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions

Andrii Mironchenko and Christophe Prieur
SIAM Review 62 (3) 529 (2020)
DOI: 10.1137/19M1291248
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Refined exponential stability analysis of a coupled system * *The paper was partially supported by the ANR projects LimICoS and SCIDIS. Corresponding author. Fax +33-561336411.

Mohammed Safi, Lucie Baudouin and Alexandre Seuret
IFAC-PapersOnLine 50 (1) 11972 (2017)
DOI: 10.1016/j.ifacol.2017.08.1758
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PDE Observer Design for Counter-Current Heat Flows in a Heat-Exchanger

Fairouz Zobiri, Emmanuel Witrant and François Bonne
IFAC-PapersOnLine 50 (1) 7127 (2017)
DOI: 10.1016/j.ifacol.2017.08.548
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Trajectory tracking for a system of two linear hyperbolic PDEs with uncertainties

Jean Auriol and Florent Di Meglio
IFAC-PapersOnLine 50 (1) 7089 (2017)
DOI: 10.1016/j.ifacol.2017.08.1357
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Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms

Martin Gugat, Vincent Perrollaz and Lionel Rosier
Journal of Evolution Equations 18 (3) 1471 (2018)
DOI: 10.1007/s00028-018-0449-z
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Stabilization of a linear hyperbolic PDE with actuator and sensor dynamics

Henrik Anfinsen and Ole Morten Aamo
Automatica 95 104 (2018)
DOI: 10.1016/j.automatica.2018.05.019
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Input-to-State Stability for PDEs

Iasson Karafyllis and Miroslav Krstic
Communications and Control Engineering, Input-to-State Stability for PDEs 39 (2019)
DOI: 10.1007/978-3-319-91011-6_3
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Input-to-State Stability for PDEs

Iasson Karafyllis and Miroslav Krstic
Communications and Control Engineering, Input-to-State Stability for PDEs 215 (2019)
DOI: 10.1007/978-3-319-91011-6_9
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Output feedback boundary control of 2×2 semilinear hyperbolic systems

Timm Strecker and Ole Morten Aamo
Automatica 83 290 (2017)
DOI: 10.1016/j.automatica.2017.06.026
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Tracking in Minimum Time in General Linear Hyperbolic PDEs Using Collocated Sensing and Control

Henrik Anfinsen and Ole Morten Aamo
IFAC-PapersOnLine 49 (8) 234 (2016)
DOI: 10.1016/j.ifacol.2016.07.447
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Numerical Feedback Stabilization with Applications to Networks

Simone Göttlich and Peter Schillen
Discrete Dynamics in Nature and Society 2017 1 (2017)
DOI: 10.1155/2017/6896153
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Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws

Ababacar Diagne, Georges Bastin and Jean-Michel Coron
Automatica 48 (1) 109 (2012)
DOI: 10.1016/j.automatica.2011.09.030
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Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm

Jean-Michel Coron and Georges Bastin
SIAM Journal on Control and Optimization 53 (3) 1464 (2015)
DOI: 10.1137/14097080X
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On the relation of delay equations to first-order hyperbolic partial differential equations

Iasson Karafyllis and Miroslav Krstic
ESAIM: Control, Optimisation and Calculus of Variations 20 (3) 894 (2014)
DOI: 10.1051/cocv/2014001
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Feedback Stabilization of a Food Extrusion Process Described by 1D PDEs Defined on Coupled Time-Varying Spatial Domains

Mamadou DIAGNE, Peipei SHANG and Zhiqiang WANG
IFAC-PapersOnLine 48 (12) 51 (2015)
DOI: 10.1016/j.ifacol.2015.09.352
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A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws

J.-M. Coron, B. d'Andrea-Novel and G. Bastin
IEEE Transactions on Automatic Control 52 (1) 2 (2007)
DOI: 10.1109/TAC.2006.887903
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On the finite-time boundary dissipative for a class of hyperbolic systems. The networks example

Ghada Ben Belgacem and Chaker Jammazi
IFAC-PapersOnLine 49 (8) 186 (2016)
DOI: 10.1016/j.ifacol.2016.07.435
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Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs

Long Hu, Florent Di Meglio, Rafael Vazquez and Miroslav Krstic
IEEE Transactions on Automatic Control 61 (11) 3301 (2016)
DOI: 10.1109/TAC.2015.2512847
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Stability and Boundary Stabilization of 1-D Hyperbolic Systems

Georges Bastin and Jean-Michel Coron
Progress in Nonlinear Differential Equations and Their Applications, Stability and Boundary Stabilization of 1-D Hyperbolic Systems 88 117 (2016)
DOI: 10.1007/978-3-319-32062-5_4
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Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input

Florent Di Meglio, Rafael Vazquez and Miroslav Krstic
IEEE Transactions on Automatic Control 58 (12) 3097 (2013)
DOI: 10.1109/TAC.2013.2274723
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An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems

Pierre-Olivier Lamare, Antoine Girard and Christophe Prieur
ESAIM: Control, Optimisation and Calculus of Variations 22 (4) 1236 (2016)
DOI: 10.1051/cocv/2016038
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Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems

Jean-Michel Coron, Georges Bastin and Brigitte d'Andréa-Novel
SIAM Journal on Control and Optimization 47 (3) 1460 (2008)
DOI: 10.1137/070706847
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Multivariable boundary PI control and regulation of a fluid flow system

Gauthier Sallet and Cheng-Zhong Xu
Mathematical Control and Related Fields 4 (4) 501 (2014)
DOI: 10.3934/mcrf.2014.4.501
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An Adaptive Observer Design for $n+1$ Coupled Linear Hyperbolic PDEs Based on Swapping

Henrik Anfinsen, Mamadou Diagne, Ole Morten Aamo and Miroslav Krstic
IEEE Transactions on Automatic Control 61 (12) 3979 (2016)
DOI: 10.1109/TAC.2016.2530624
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Minimum time control of heterodirectional linear coupled hyperbolic PDEs

Jean Auriol and Florent Di Meglio
Automatica 71 300 (2016)
DOI: 10.1016/j.automatica.2016.05.030
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Stabilization of torsional vibration in oilwell drillstring system

Samir Toumi, Lotfi Beji, Rhouma Mlayeh and Azgal Abichou
European Journal of Control 35 19 (2017)
DOI: 10.1016/j.ejcon.2017.03.002
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Lyapunov exponential stability of linear hyperbolic systems of balance laws

Ababacar Diagne, Georges Bastin and Jean-Michel Coron
IFAC Proceedings Volumes 44 (1) 13320 (2011)
DOI: 10.3182/20110828-6-IT-1002.01506
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Feedback Stabilization for the Mass Balance Equations of an Extrusion Process

Mamadou Diagne, Peipei Shang and Zhiqiang Wang
IEEE Transactions on Automatic Control 61 (3) 760 (2016)
DOI: 10.1109/TAC.2015.2444232
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Infinite-Dimensional Predictive Control for Hyperbolic Systems

Van Thang Pham, Didier Georges and Gildas Besançon
SIAM Journal on Control and Optimization 52 (6) 3592 (2014)
DOI: 10.1137/110838200
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Fuzzy output tracking control of semi-linear first-order hyperbolic PDE systems with matched perturbations

Jun-Wei Wang and Huai-Ning Wu
Fuzzy Sets and Systems 254 47 (2014)
DOI: 10.1016/j.fss.2014.03.007
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Boundary Control of a Class of Hyperbolic Systems

A. Chapelon and C.-Z. Xu
European Journal of Control 9 (6) 589 (2003)
DOI: 10.3166/ejc.9.589-604
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Lyapunov-Based Boundary Control for A Class of Hyperbolic Lotka–Volterra Systems

L. Pavel and L. Chang
IEEE Transactions on Automatic Control 57 (3) 701 (2012)
DOI: 10.1109/TAC.2011.2168909
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Abstract State-Space Models for a Class of Linear Hyperbolic Systems of Balance Laws

Krzysztof Bartecki
Reports on Mathematical Physics 76 (3) 339 (2015)
DOI: 10.1016/S0034-4877(15)30037-9
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Output Feedback Stabilization for a Scalar Conservation Law with a Nonlocal Velocity

Jean-Michel Coron and Zhiqiang Wang
SIAM Journal on Mathematical Analysis 45 (5) 2646 (2013)
DOI: 10.1137/120902203
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Numerical discretization of boundary control problems for systems of balance laws: Feedback stabilization

Simone Göttlich and Peter Schillen
European Journal of Control 35 11 (2017)
DOI: 10.1016/j.ejcon.2017.02.002
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Disturbance rejection in general heterodirectional 1-D linear hyperbolic systems using collocated sensing and control

Henrik Anfinsen and Ole Morten Aamo
Automatica 76 230 (2017)
DOI: 10.1016/j.automatica.2016.10.027
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Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method

Abdoua Tchousso, Thibaut Besson and Cheng-Zhong Xu
ESAIM: Control, Optimisation and Calculus of Variations 15 (2) 403 (2009)
DOI: 10.1051/cocv:2008033
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Finite-Time Stabilization of $2\times2$ Hyperbolic Systems on Tree-Shaped Networks

Vincent Perrollaz and Lionel Rosier
SIAM Journal on Control and Optimization 52 (1) 143 (2014)
DOI: 10.1137/130910762
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OBSERVER DESIGN USING BOUNDARY INJECTIONS FOR PIPELINE MONITORING AND LEAK DETECTION

Ole Morten Aamo, Jørgen Salvesen and Bjarne A. Foss
IFAC Proceedings Volumes 39 (2) 53 (2006)
DOI: 10.3182/20060402-4-BR-2902.00053
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Fuzzy Control Design for Nonlinear ODE-Hyperbolic PDE-Cascaded Systems: A Fuzzy and Entropy-Like Lyapunov Function Approach

Jun-Wei Wang, Huai-Ning Wu and Han-Xiong Li
IEEE Transactions on Fuzzy Systems 22 (5) 1313 (2014)
DOI: 10.1109/TFUZZ.2013.2291569
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Some extended Wirtinger׳s inequalities and distributed proportional-spatial integral control of distributed parameter systems with multi-time delays

Jun-Wei Wang and Huai-Ning Wu
Journal of the Franklin Institute 352 (10) 4423 (2015)
DOI: 10.1016/j.jfranklin.2015.06.011
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Wind instruments as time delay systems. Part II: control and estimation*

B. d'Andréa-Novel, J.-M. Coron, B. Fabre and T. Hélie
IFAC Proceedings Volumes 42 (14) 290 (2009)
DOI: 10.3182/20090901-3-RO-4009.00047
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Numerical Computation of Lyapunov Function for Hyperbolic PDE using LMI Formulation and Polytopic Embeddings**This work has been partially supported by the LabEx PERSYVAL-Lab ANR-11-LABX-0025.

Pierre-Olivier Lamare, Antoine Girard and Christophe Prieur
IFAC-PapersOnLine 48 (26) 7 (2015)
DOI: 10.1016/j.ifacol.2015.11.105
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Boundary feedback stabilization and Riesz basis property of a 1-d first order hyperbolic linear system with L∞-coefficients

Boumediène Chentouf and Jun-Min Wang
Journal of Differential Equations 246 (3) 1119 (2009)
DOI: 10.1016/j.jde.2008.08.010
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Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws

Mapundi K. Banda and Michael Herty
Mathematical Control and Related Fields 3 (2) 121 (2013)
DOI: 10.3934/mcrf.2013.3.121
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Boundary Parameter and State Estimation in General Linear Hyperbolic PDEs

Henrik Anfinsen, Mamadou Diagne, Ole Morten Aamo and Miroslav Krstic
IFAC-PapersOnLine 49 (8) 104 (2016)
DOI: 10.1016/j.ifacol.2016.07.426
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Control of shallow water and sediment continuity coupled system

Ababacar Diagne and Abdou Sène
Mathematics of Control, Signals, and Systems 25 (3) 387 (2013)
DOI: 10.1007/s00498-012-0101-3
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Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping

Jean-Michel Coron, Rafael Vazquez, Miroslav Krstic and Georges Bastin
SIAM Journal on Control and Optimization 51 (3) 2005 (2013)
DOI: 10.1137/120875739
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Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems

Jean-Michel Coron and Hoai-Minh Nguyen
SIAM Journal on Mathematical Analysis 47 (3) 2220 (2015)
DOI: 10.1137/140976625
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Estimation of boundary parameters in general heterodirectional linear hyperbolic systems

Henrik Anfinsen, Mamadou Diagne, Ole Morten Aamo and Miroslav Krstic
Automatica 79 185 (2017)
DOI: 10.1016/j.automatica.2017.01.015
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Classical Solutions in Sobolev Spaces for a Class of Hyperbolic Lotka--Volterra Systems

Lacra Pavel
SIAM Journal on Control and Optimization 51 (3) 2132 (2013)
DOI: 10.1137/090767303
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Marcum -functions and explicit kernels for stabilization of linear hyperbolic systems with constant coefficients

Rafael Vazquez and Miroslav Krstic
Systems & Control Letters 68 33 (2014)
DOI: 10.1016/j.sysconle.2014.02.008
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Two-Sided Boundary Stabilization of Heterodirectional Linear Coupled Hyperbolic PDEs

Jean Auriol and Florent Di Meglio
IEEE Transactions on Automatic Control 63 (8) 2421 (2018)
DOI: 10.1109/TAC.2017.2763320
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Boundary Feedback Stabilization of a Class of Coupled Hyperbolic Equations With Nonlocal Terms

Lingling Su, Jun-Min Wang and Miroslav Krstic
IEEE Transactions on Automatic Control 63 (8) 2633 (2018)
DOI: 10.1109/TAC.2017.2767824
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Review on computational methods for Lyapunov functions

Peter Giesl and Sigurdur Hafstein
Discrete and Continuous Dynamical Systems - Series B 20 (8) 2291 (2015)
DOI: 10.3934/dcdsb.2015.20.2291
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Stability of a heat exchanger feedback control system using the circle criterion

P. Grabowski
International Journal of Control 80 (9) 1388 (2007)
DOI: 10.1080/00207170701291744
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Control of shallow waves of two unmixed fluids by backstepping

Mamadou Diagne, Shu-Xia Tang, Ababacar Diagne and Miroslav Krstic
Annual Reviews in Control 44 211 (2017)
DOI: 10.1016/j.arcontrol.2017.09.003
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On the relaxation approximation of boundary control of the isothermal Euler equations

M. Dick, M. Gugat, M. Herty and S. Steffensen
International Journal of Control 85 (11) 1766 (2012)
DOI: 10.1080/00207179.2012.703787
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Global Feedback Stabilization for a Class of Nonlocal Transport Equations: The Continuous and Discrete Case

Wenbin Chen, Chang Liu and Zhiqiang Wang
SIAM Journal on Control and Optimization 55 (2) 760 (2017)
DOI: 10.1137/15M1048914
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Boundary stabilization of hyperbolic balance laws with characteristic boundaries

Wen-An Yong
Automatica 101 252 (2019)
DOI: 10.1016/j.automatica.2018.12.003
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Heat transfer—a review of 2002 literature

R.J. Goldstein, E.R.G. Eckert, W.E. Ibele, et al.
International Journal of Heat and Mass Transfer 48 (5) 819 (2005)
DOI: 10.1016/j.ijheatmasstransfer.2004.10.011
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Adaptive Control of Hyperbolic PDEs

Henrik Anfinsen and Ole Morten Aamo
Communications and Control Engineering, Adaptive Control of Hyperbolic PDEs 3 (2019)
DOI: 10.1007/978-3-030-05879-1_1
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Stability analysis of coupled linear ODE-hyperbolic PDE systems with two time scales

Ying Tang and Guilherme Mazanti
Automatica 85 386 (2017)
DOI: 10.1016/j.automatica.2017.07.052
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Stable Day-to-Day Dynamics for Departure Time Choice

Wen-Long Jin
Transportation Science (2020)
DOI: 10.1287/trsc.2019.0919
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Adaptive boundary observer design for linear hyperbolic systems; Application to estimation in heat exchangers

Mohammad Ghousein, Emmanuel Witrant, Viren Bhanot and Paolo Petagna
Automatica 114 108824 (2020)
DOI: 10.1016/j.automatica.2020.108824
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Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs

Jean Auriol and Florent Di Meglio
Automatica 115 108896 (2020)
DOI: 10.1016/j.automatica.2020.108896
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Articles citing this article

Cited article:

Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems

This article has been cited by the following article(s):

Stability Analysis for a Class of Linear 2x2 Hyperbolic PDEs Using a Backstepping Transform

ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws

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Rational Transfer Function Model for a Double-Pipe Parallel-Flow Heat Exchanger

Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions

Refined exponential stability analysis of a coupled system * *The paper was partially supported by the ANR projects LimICoS and SCIDIS. Corresponding author. Fax +33-561336411.

PDE Observer Design for Counter-Current Heat Flows in a Heat-Exchanger

Trajectory tracking for a system of two linear hyperbolic PDEs with uncertainties

Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms

Stabilization of a linear hyperbolic PDE with actuator and sensor dynamics

Input-to-State Stability for PDEs

Input-to-State Stability for PDEs

Output feedback boundary control of 2×2 semilinear hyperbolic systems

Tracking in Minimum Time in General Linear Hyperbolic PDEs Using Collocated Sensing and Control

Numerical Feedback Stabilization with Applications to Networks

Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws

Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm

On the relation of delay equations to first-order hyperbolic partial differential equations

Feedback Stabilization of a Food Extrusion Process Described by 1D PDEs Defined on Coupled Time-Varying Spatial Domains

A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws

On the finite-time boundary dissipative for a class of hyperbolic systems. The networks example

Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs

Stability and Boundary Stabilization of 1-D Hyperbolic Systems

Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input

An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems

Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems

Multivariable boundary PI control and regulation of a fluid flow system

An Adaptive Observer Design for $n+1$ Coupled Linear Hyperbolic PDEs Based on Swapping

Minimum time control of heterodirectional linear coupled hyperbolic PDEs

Stabilization of torsional vibration in oilwell drillstring system

Lyapunov exponential stability of linear hyperbolic systems of balance laws

Feedback Stabilization for the Mass Balance Equations of an Extrusion Process

Infinite-Dimensional Predictive Control for Hyperbolic Systems

Fuzzy output tracking control of semi-linear first-order hyperbolic PDE systems with matched perturbations

Boundary Control of a Class of Hyperbolic Systems

Lyapunov-Based Boundary Control for A Class of Hyperbolic Lotka–Volterra Systems

Abstract State-Space Models for a Class of Linear Hyperbolic Systems of Balance Laws

Output Feedback Stabilization for a Scalar Conservation Law with a Nonlocal Velocity

Numerical discretization of boundary control problems for systems of balance laws: Feedback stabilization

Disturbance rejection in general heterodirectional 1-D linear hyperbolic systems using collocated sensing and control

Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method

Finite-Time Stabilization of $2\times2$ Hyperbolic Systems on Tree-Shaped Networks

OBSERVER DESIGN USING BOUNDARY INJECTIONS FOR PIPELINE MONITORING AND LEAK DETECTION

Fuzzy Control Design for Nonlinear ODE-Hyperbolic PDE-Cascaded Systems: A Fuzzy and Entropy-Like Lyapunov Function Approach

Some extended Wirtinger׳s inequalities and distributed proportional-spatial integral control of distributed parameter systems with multi-time delays

Wind instruments as time delay systems. Part II: control and estimation*

Numerical Computation of Lyapunov Function for Hyperbolic PDE using LMI Formulation and Polytopic Embeddings**This work has been partially supported by the LabEx PERSYVAL-Lab ANR-11-LABX-0025.

Boundary feedback stabilization and Riesz basis property of a 1-d first order hyperbolic linear system with L∞-coefficients

Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws

Boundary Parameter and State Estimation in General Linear Hyperbolic PDEs

Control of shallow water and sediment continuity coupled system

Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping

Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems

Estimation of boundary parameters in general heterodirectional linear hyperbolic systems

Classical Solutions in Sobolev Spaces for a Class of Hyperbolic Lotka--Volterra Systems

Marcum -functions and explicit kernels for stabilization of linear hyperbolic systems with constant coefficients

Two-Sided Boundary Stabilization of Heterodirectional Linear Coupled Hyperbolic PDEs

Boundary Feedback Stabilization of a Class of Coupled Hyperbolic Equations With Nonlocal Terms

Review on computational methods for Lyapunov functions

Stability of a heat exchanger feedback control system using the circle criterion

Control of shallow waves of two unmixed fluids by backstepping

On the relaxation approximation of boundary control of the isothermal Euler equations

Global Feedback Stabilization for a Class of Nonlocal Transport Equations: The Continuous and Discrete Case

Boundary stabilization of hyperbolic balance laws with characteristic boundaries

Heat transfer—a review of 2002 literature

Adaptive Control of Hyperbolic PDEs

Stability analysis of coupled linear ODE-hyperbolic PDE systems with two time scales

Stable Day-to-Day Dynamics for Departure Time Choice

Adaptive boundary observer design for linear hyperbolic systems; Application to estimation in heat exchangers

Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs