Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 66
Number of page(s) 35
DOI https://doi.org/10.1051/cocv/2023057
Published online 11 August 2023
  1. L. Benvenuti, L. Farina and B.D.O. Anderson, The positive side of filters: a summary. IEEE Circ. Sys. Mag. 1 (2001) 32–36. [CrossRef] [Google Scholar]
  2. F. Blanchini, P. Colaneri and M.E. Valcher, Switched linear positive systems. Found. Trends Syst. Control 2 (2015) 101–273. [CrossRef] [Google Scholar]
  3. K.L. Bichitra and N.B. Swaroop, New global asymptotic stability conditions for a class of nonlinear time-varying fractional systems. Eur. J. Control 63 (2022) 97–106. [CrossRef] [MathSciNet] [Google Scholar]
  4. C. Briat, Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: ℓ1-gain and ℓ-gain characterization. Int. J. Robust Nonlinear Control 23 (2013) 1932–1954. [CrossRef] [Google Scholar]
  5. H. Brunner, Volterra Integral Equations: An Introduction to Theory and applications. Cambridge University Press (2017). [CrossRef] [Google Scholar]
  6. E. Carson and C. Cobelli, Modelling Methodology for Physiology and Medicine. Academic Press, San Diego (2001). [Google Scholar]
  7. N.D. Cong, H.T. Tuan, Generation of nonlocal fractional dynamical systems by fractional differential equations. J. Integral Eq. Applic. 29 (2017) 585–608. [Google Scholar]
  8. N.D. Cong, H.T. Tuan and H. Trinh, On asymptotic properties of solutions to fractional differential equations. J. Math. Anal. Applic. 484 (2020) 123759. [CrossRef] [Google Scholar]
  9. P.G. Coxson and H. Shapiro, Positive reachability and controllability of positive systems. Linear Algebra Appl. 94 (1987) 35–53. [CrossRef] [MathSciNet] [Google Scholar]
  10. Y. Cui, J. Shen, W. Zhang, Z. Feng and X. Gong, Positivity and stability analysis of homogeneous coupled differential-difference equations with time-varying delays. IEEE Trans. Automatic Control 67 (2022) 5493–5500. [CrossRef] [MathSciNet] [Google Scholar]
  11. K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Lecture Notes in Mathematics, 2004. Springer-Verlag, Berlin (2010). [Google Scholar]
  12. R.A.C. Ferreira, Sign of the solutions of linear fractional differential equations and some applications. Vietnam J. Math. 51 (2023) 451–461. [CrossRef] [MathSciNet] [Google Scholar]
  13. H.R. Feyzmahdavian, T. Charalambous and M. Johansson, Asymptotic stability and decay rates of homogeneous positive systems with bounded and unbounded delays. SIAM J. Control Optim. 52 (2014) 2623–2650. [CrossRef] [MathSciNet] [Google Scholar]
  14. J.A. Gallegos, N. Aguila-Camacho and M. Duarte-Mermoud, Vector Lyapunov-like functions for multi-order fractional systems with multiple time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 83 (2020) 105089. [CrossRef] [MathSciNet] [Google Scholar]
  15. U. Graf, Applied Laplace Transforms and z-Transforms for Scientists and Engineers. Springer Basel AG (2004). [CrossRef] [Google Scholar]
  16. K. Gu, and S.I. Niculescu, Stability analysis of time-delay systems: a Lyapunov approach, in Advanced Topics in Control Systems Theory. Lecture Notes in Control and Information Science, edited by A. Loría, F. Lamnabhi-Lagarrigue and E. Panteley, Vol. 328. Springer, London (2006). [Google Scholar]
  17. K. Gu, Stability problem of systems with multiple delay channels. Automatica 46 (2010) 743–751. [CrossRef] [MathSciNet] [Google Scholar]
  18. W.M. Haddad and V. Chellaboina, Stability theory for nonnegative and compartmental dynamical systems with time delay. Syst. Control Lett. 51 (2004) 355–361. [CrossRef] [Google Scholar]
  19. W.M. Haddad, V. Chellaboina and Q. Hui, Nonnegative and Compartmental Dynamical Systems. Princeton University Press, Princeton, New Jersey (2010). [CrossRef] [Google Scholar]
  20. J.K. Hale and S.M.V. Lunel, Introduction to Functional Differential Equations. Springer Verlag, Berlin (1993). [CrossRef] [Google Scholar]
  21. E. Hernandez-Vargas, R. Middleton, P. Colaneri and F. Blanchini, Discrete-time control for switched positive systems with application to mitigating viral escape. Int. J. Robust Nonlinear Control. 21 (2011) 1093–1111. [CrossRef] [Google Scholar]
  22. I.T. Huseynov, and N.I. Mahmudov, Analysis of positive fractional-order neutral time-delay systems. J. Franklin Inst. 359 (2022) 294–330. [CrossRef] [MathSciNet] [Google Scholar]
  23. J. Jia, F. Wang and Z. Zeng, Global stabilization of fractional-order memristor-based neural networks with incommensurate orders and multiple time-varying delays: a positive-system-based approach. Nonlinear Dyn. 104 (2021) 2303–2329. [CrossRef] [Google Scholar]
  24. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Vol. 191 of Mathematics in Science and Engineering. Academic Press, Inc., Boston, Massachusetts (1993). [Google Scholar]
  25. A. Kubica and K. Ryszewska, Fractional diffusion equation with distributed-order Caputo derivative. J. Integral Eq. Applic. 31 (2019) 195–243. [Google Scholar]
  26. V. Lakshmikantham, S. Leela and J.V Vasundhara Devi, Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge (2009). [Google Scholar]
  27. D.G. Luenberger, Introduction to Dynamical Systems. John Wiley & Sons Inc. (1979). [Google Scholar]
  28. F. Mazenc, H. Ito and P. Pepe, Construction of Lyapunov functionals for coupled differential and continuous time difference equations. 52nd IEEE Conference on Decision and Control, 2013. [Google Scholar]
  29. W. Michiels and S.I. Niculescu, Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach. Advances in Design and Control, Vol. 12. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pennsylvania (2007). [Google Scholar]
  30. Y. Moreno, R. Pastor-Satorras and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks. Eur. Phys. J. B: Condensed Matter Complex Syst. 26 (2002) 521–529. [Google Scholar]
  31. S.I. Niculescu, Delay Effects On Stability: A Robust Control Approach. Springer, Berlin (2001). [Google Scholar]
  32. J.W. Nieuwenhuis, Some results about a Leontieff-type model, in Frequency Domain and STATE Space Methods for Linear Systems, edited by C.I. Byrnes and Lindquist A. Elsevier Science (1986) 213–225. [Google Scholar]
  33. P.H.A. Ngoc, On positivity and stability of linear Volterra systems with delay. SIAM J. Control Optim. 48 (2009) 1939–1960. [CrossRef] [MathSciNet] [Google Scholar]
  34. P.N. Pathirana, P.T. Nam and H. Trinh, Stability of positive coupled differential-difference equations with unbounded timevarying delays. Automatica 92 (2018) 259–263. [CrossRef] [Google Scholar]
  35. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Mathematics in Science and Engineering, Vol. 198. Academic Press, San Diego, CA, USA (1999). [Google Scholar]
  36. A. Rantzer and M.E. Valcher, A tutorial on positive systems and large scale control. 2018 IEEE Conference on Decision and Control (CDC). (2018) 3686–3697 [CrossRef] [Google Scholar]
  37. V. Rasvan and S.I. Niculescu, Oscillations in lossless propagation models: a Liapunov-Krasovskii approach. IMA J. Math. Control Inform. 19 (2002) 157–172. [CrossRef] [MathSciNet] [Google Scholar]
  38. V. Rasvan, Functional Differential Equations of Lossless Propagation and Almost Linear Behavior, Plenary Lecture, edited by C. Manes and P. Pepe. Proceedings of the 6th IFAC Workshop on Time-Delay Systems, L’Aquila, Italy, 2006, IFAC- PapersOnline, Vol. 6, Part 1. [Google Scholar]
  39. J. Shen and J. Lam, ℓ/ℓ-gain analysis for positive linear systems with unbounded time-varying delays. IEEE Trans. Automatic Control 60 (2015) 857–862. [CrossRef] [MathSciNet] [Google Scholar]
  40. J. Shen and W.X. Zheng, Positivity and stability of coupled differentialdifference equations with time-varying delays. Automatica 57 (2015) 123–127. [CrossRef] [Google Scholar]
  41. J. Shen and J. Lam, Stability and performance analysis for positive fractional-order systems with time-varying delays. IEEE Trans. Automat. Control. 61 (2016) 2676–2681. [CrossRef] [MathSciNet] [Google Scholar]
  42. H.T. Tuan and H. Trinh, A qualitative theory of time delay nonlinear fractional-order systems. SIAM J. Control Optim. 58 1491–1518. [Google Scholar]
  43. H.T. Tuan, H. Trinh and J. Lam, Positivity and stability of mixed fractional-order systems with unbounded delays: necessary and sufficient conditions. Int. J. Robust Nonlinear Control 31 37–50. [Google Scholar]
  44. H.T. Tuan, Smallest asymptotic bound of solutions to positive mixed fractional-order inhomogeneous linear systems with time-varying delays. J. Franklin Inst. 359 (2022) 3768–3778. [CrossRef] [MathSciNet] [Google Scholar]
  45. G. Vainikko, Which functions are fractionally differentiable? Z. Anal. Anwend. 35 (2016) 465–487. [CrossRef] [MathSciNet] [Google Scholar]
  46. D. Del Vecchio and R.M. Murray, Biomolecular Feedback Systems. Princeton University Press, Princeton, New Jersey (2014). [CrossRef] [Google Scholar]
  47. Q. Xiao, Z. Zeng, T. Huang and Frank L. Lewis, Positivity and stability of coupled differential–difference equations with time-varying delay on time scales. Automatica 131 (2021) 109774. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.