Akademik Veri Yönetim Sistemi
Analysis and Applied Mathematics, Allaberen Ashyralyev,Michael Ruzhansky,Makhmud A. Sadybekov, Editör, Birkhäuser , Zug, ss.231-239, 2024
This chapter addresses some open questions about how to guarantee the exponential stability of switched time-delay systems by using constrained switching techniques. When extended to switched systems, the Lyapunov-Krasovskii, Lyapunov-Razumikhin, and Lyapunov-Halanay methods in time-delay systems have the potential to result in some unique average dwell-time bounds that are well-known in a delay-free context. We start presenting a result by using the family of Lyapunov-Krasovskii functionals, which is a direct extension of a well-known result in finite-dimensional systems. We also provide the results given by using the Lyapunov-Razumikhin methodology. After presenting the results in the literature, we address the question of whether the Lyapunov-Razumikhin method may have alternative extensions in switched time-delay systems. We conclude the chapter by addressing the questions of whether Lyapunov-Halanay methods can also be used to establish the exponential stability of switched time-delay systems and how a mix of all these methods can be used to establish the exponential stability of switched time-delay systems.