Lyapunov–Krasovskii functional approach for h-stability
analysis of linear continuous-time systems.
Main Article Content
Abstract
In this study, we provide new adequate conditions to demonstrate the h-stability of linear
continuous-time systems using the Lyapunov-Krasovskii functional approach, which may be
seen as an extension of exponential stability. Additionally, we present a few simulation-based
examples to illustrate the relevance of the obtained conclusions
Keywords
h−stability, Lyapunov–Krasovskii functional, continuous-time systems, linear matrix inequalities.
Article Details
References
[1] M. Pinto, Stability of nonlinear differential systems, Appl. Anal. 43 (1992), 1–20.
[2] M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161–175.
[3] R. Medina and M. Pinto, Stability of nonlinear difference equations, in: G. S. Ladde et al. (eds.), Dynamic Systems and Applications, Vol. 2., Proceedings of the 2nd International Conference, Morehouse
College, Atlanta, GA, USA, May 24–27, 1995, Dynamic Publishers, Atlanta, GA, 1996, pp. 397–404.
[4] H. Damak, M. A. Hammami and A. Kicha, A converse theorem on practical h−stability of nonlinear
systems, Mediterr. J. Math. 17, 88(2020), https://doi.org/10.1007/s00009-020-01518-2.
[5] A. B. Makhlouf and M. A. Hammami, A nonlinear inequality and application to global asymptotic
stability of perturbed systems, Math. Method. Appl. Sci. 38 (2015), 2496–2505.
[6] B. B. Hamed, Z. H. Salem and M. A. Hammami, Stability of nonlinear time-varying perturbed differential equations, Nonlinear Dyn. 73 (2013), 1353–1365.
[2] M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161–175.
[3] R. Medina and M. Pinto, Stability of nonlinear difference equations, in: G. S. Ladde et al. (eds.), Dynamic Systems and Applications, Vol. 2., Proceedings of the 2nd International Conference, Morehouse
College, Atlanta, GA, USA, May 24–27, 1995, Dynamic Publishers, Atlanta, GA, 1996, pp. 397–404.
[4] H. Damak, M. A. Hammami and A. Kicha, A converse theorem on practical h−stability of nonlinear
systems, Mediterr. J. Math. 17, 88(2020), https://doi.org/10.1007/s00009-020-01518-2.
[5] A. B. Makhlouf and M. A. Hammami, A nonlinear inequality and application to global asymptotic
stability of perturbed systems, Math. Method. Appl. Sci. 38 (2015), 2496–2505.
[6] B. B. Hamed, Z. H. Salem and M. A. Hammami, Stability of nonlinear time-varying perturbed differential equations, Nonlinear Dyn. 73 (2013), 1353–1365.