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## Existence of classical solutions and feedback stabilization for the flow in gas networks

ESAIM: COCV, 17 1 (2011) 28-51
Published online: 2009-08-11

## System Modeling and Optimization

Martin Gugat, Markus Dick and Günter Leugering
IFIP Advances in Information and Communication Technology, System Modeling and Optimization 391 255 (2013)
DOI: 10.1007/978-3-642-36062-6_26

## Trends in PDE Constrained Optimization

Markus Dick, Martin Gugat, Michael Herty, et al.
International Series of Numerical Mathematics, Trends in PDE Constrained Optimization 165 487 (2014)
DOI: 10.1007/978-3-319-05083-6_31

## Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

Martin Gugat
SpringerBriefs in Electrical and Computer Engineering, Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems 29 (2015)
DOI: 10.1007/978-3-319-18890-4_3

## Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

Martin Gugat
SpringerBriefs in Electrical and Computer Engineering, Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems 47 (2015)
DOI: 10.1007/978-3-319-18890-4_4

## Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

Martin Gugat
SpringerBriefs in Electrical and Computer Engineering, Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems 69 (2015)
DOI: 10.1007/978-3-319-18890-4_5

## Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

Martin Gugat
SpringerBriefs in Electrical and Computer Engineering, Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems 1 (2015)
DOI: 10.1007/978-3-319-18890-4_1

## Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

Martin Gugat
SpringerBriefs in Electrical and Computer Engineering, Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems 3 (2015)
DOI: 10.1007/978-3-319-18890-4_2

## Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

Martin Gugat
SpringerBriefs in Electrical and Computer Engineering, Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems 89 (2015)
DOI: 10.1007/978-3-319-18890-4_6

## Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

Martin Gugat
SpringerBriefs in Electrical and Computer Engineering, Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems 127 (2015)
DOI: 10.1007/978-3-319-18890-4_7

## Feedback boundary control of linear hyperbolic equations with stiff source term

Michael Herty and Hui Yu
International Journal of Control 91 (1) 230 (2018)
DOI: 10.1080/00207179.2016.1276635

## Output feedback boundary control of series interconnections of 2 × 2 semilinear hyperbolic systems

Timm Strecker and Ole Morten Aamo
IFAC-PapersOnLine 50 (1) 663 (2017)
DOI: 10.1016/j.ifacol.2017.08.121

## 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

## Lipschitz solutions of initial boundary value problems for balance laws

Martin Gugat and Stefan Ulbrich
Mathematical Models and Methods in Applied Sciences 28 (05) 921 (2018)
DOI: 10.1142/S0218202518500240

## Stationary Gas Networks with Compressor Control and Random Loads: Optimization with Probabilistic Constraints

Martin Gugat and Michael Schuster
Mathematical Problems in Engineering 2018 1 (2018)
DOI: 10.1155/2018/7984079

## Electric transmission lines: Control and numerical discretization

Simone Göttlich, Michael Herty and Peter Schillen
Optimal Control Applications and Methods 37 (5) 980 (2016)
DOI: 10.1002/oca.2219

## 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

## 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

## Singular Perturbation Approximation of Linear Hyperbolic Systems of Balance Laws

Ying Tang, Christophe Prieur and Antoine Girard
IEEE Transactions on Automatic Control 61 (10) 3031 (2016)
DOI: 10.1109/TAC.2015.2499444

## 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

## H 2-stabilization of the Isothermal Euler equations: a Lyapunov function approach

Martin Gugat, Günter Leugering, Simona Tamasoiu and Ke Wang
Chinese Annals of Mathematics, Series B 33 (4) 479 (2012)
DOI: 10.1007/s11401-012-0727-y

## 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

## 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

## A strict $H^1$-Lyapunov function and feedback stabilization for the isothermal Euler equations with friction

Markus Dick, Martin Gugat and Günter Leugering
Numerical Algebra, Control and Optimization 1 (2) 225 (2011)
DOI: 10.3934/naco.2011.1.225

## Gas Flow in Fan-Shaped Networks: Classical Solutions and Feedback Stabilization

Martin Gugat, Markus Dick and Günter Leugering
SIAM Journal on Control and Optimization 49 (5) 2101 (2011)
DOI: 10.1137/100799824

## Networks of pipelines for gas with nonconstant compressibility factor: stationary states

Martin Gugat, Rüdiger Schultz and David Wintergerst
Computational and Applied Mathematics 37 (2) 1066 (2018)
DOI: 10.1007/s40314-016-0383-z

## Feedback Stabilization of Controlled Dynamical Systems

Christophe Prieur and Aneel Tanwani
Lecture Notes in Control and Information Sciences, Feedback Stabilization of Controlled Dynamical Systems 473 201 (2017)
DOI: 10.1007/978-3-319-51298-3_8

## 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

## 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

## 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

## Stationary states in gas networks

Günter Leugering, Markus Hirsch-Dick, Falk M. Hante and Martin Gugat
Networks and Heterogeneous Media 10 (2) 295 (2015)
DOI: 10.3934/nhm.2015.10.295

## Control of 2×2 linear hyperbolic systems: Backstepping-based trajectory generation and PI-based tracking

Pierre-Olivier Lamare and Nikolaos Bekiaris-Liberis
Systems & Control Letters 86 24 (2015)
DOI: 10.1016/j.sysconle.2015.09.009

## Nonlinear Stabilization in Infinite Dimension

Miroslav Krstic and Nikolaos Bekiaris-Liberis
IFAC Proceedings Volumes 46 (23) 1 (2013)
DOI: 10.3182/20130904-3-FR-2041.00061

## The exponential decay rate of generic tree of 1-d wave equations with boundary feedback controls

Genqi Xu and Yaru Xie
Networks and Heterogeneous Media 11 (3) 527 (2016)
DOI: 10.3934/nhm.2016008

## A quadratic Lyapunov function for hyperbolic density–velocity systems with nonuniform steady states

Georges Bastin and Jean-Michel Coron
Systems & Control Letters 104 66 (2017)
DOI: 10.1016/j.sysconle.2017.03.013

## Nonlinear stabilization in infinite dimension

Miroslav Krstic and Nikolaos Bekiaris-Liberis
Annual Reviews in Control 37 (2) 220 (2013)
DOI: 10.1016/j.arcontrol.2013.09.002

## Exponential stability of networks of density-flow conservation laws under PI boundary control

Georges Bastin and Jean-Michel Coron
IFAC Proceedings Volumes 46 (26) 221 (2013)
DOI: 10.3182/20130925-3-FR-4043.00029

## Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction

Martin Gugat and Markus Dick
Mathematical Control and Related Fields 1 (4) 469 (2011)
DOI: 10.3934/mcrf.2011.1.469

## 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

## Control and stabilization of $2\times 2$ hyperbolic systems on graphs

Serge Nicaise
Mathematical Control and Related Fields 7 (1) 53 (2016)
DOI: 10.3934/mcrf.2017004

## Delays and Networked Control Systems

Michael Di Loreto, Sérine Damak and Sabine Mondié
Advances in Delays and Dynamics, Delays and Networked Control Systems 6 17 (2016)
DOI: 10.1007/978-3-319-32372-5_2

## 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 1 (2016)
DOI: 10.1007/978-3-319-32062-5_1

## 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

## Event-based control of linear hyperbolic systems of conservation laws

Nicolás Espitia, Antoine Girard, Nicolas Marchand and Christophe Prieur
Automatica 70 275 (2016)
DOI: 10.1016/j.automatica.2016.04.009

## The isothermal Euler equations for ideal gas with source term: Product solutions, flow reversal and no blow up

Martin Gugat and Stefan Ulbrich
Journal of Mathematical Analysis and Applications 454 (1) 439 (2017)
DOI: 10.1016/j.jmaa.2017.04.064

## 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

## Coupling conditions for isothermal gas flow and applications to valves

Andrea Corli, Magdalena Figiel, Anna Futa and Massimiliano D. Rosini
Nonlinear Analysis: Real World Applications 40 403 (2018)
DOI: 10.1016/j.nonrwa.2017.09.005

## Boundary Feedback Stabilization of the Isothermal Euler Equations with Uncertain Boundary Data

Martin Gugat and Rüdiger Schultz
SIAM Journal on Control and Optimization 56 (2) 1491 (2018)
DOI: 10.1137/16M1090156

## On the Turnpike Phenomenon for Optimal Boundary Control Problems with Hyperbolic Systems

Martin Gugat and Falk M. Hante
SIAM Journal on Control and Optimization 57 (1) 264 (2019)
DOI: 10.1137/17M1134470

## Control of a Time Delay System Arising From Linearized Conservation Laws

Daniela Danciu, Dan Popescu and Vladimir Rasvan
IEEE Access 7 48524 (2019)
DOI: 10.1109/ACCESS.2019.2910018

## Progress in Industrial Mathematics at ECMI 2018

Stephan Gerster, Michael Herty, Michael Chertkov, Marc Vuffray and Anatoly Zlotnik
Mathematics in Industry, Progress in Industrial Mathematics at ECMI 2018 30 59 (2019)
DOI: 10.1007/978-3-030-27550-1_8

## Feedforward boundary control of 2×2 nonlinear hyperbolic systems with application to Saint-Venant equations

Georges Bastin, Jean-Michel Coron and Amaury Hayat
European Journal of Control 57 41 (2021)
DOI: 10.1016/j.ejcon.2020.11.002

## Discrete-time modeling and output regulation of gas pipeline networks

Junyao Xie and Stevan Dubljevic
Journal of Process Control 98 30 (2021)
DOI: 10.1016/j.jprocont.2020.12.002

## Numerical boundary feedback stabilisation of non-uniform hyperbolic systems of balance laws

Mapundi K. Banda and Gediyon Y. Weldegiyorgis
International Journal of Control 93 (6) 1428 (2020)
DOI: 10.1080/00207179.2018.1509133

## 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