On the time-varying Halanay inequality with applications to stability analysis of time-delay systems

Hai-fang, LI; Zhou, Bin; Hou, Ming; Duan, Guang‐Ren

doi:10.1016/j.jfranklin.2021.04.046

Cited by 18 publications

(1 citation statement)

References 34 publications

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“…Analyzing such systems is known to be very challenging, and conservative approaches have been proposed in the literature based on popular extensions of the classical Lyapunov theory established by Krasovskii and Razumikhin. Among these results, we may reference the recent contributions by Zhou and Egorov, 3 Mazenc and Malisoff, 4 and Li et al 5 Other recent approaches have leveraged trajectory-based methodologies 6 and Halanay-like inequalities 7 ; an interesting idea is to look for a continuous-time counterpart 8 of the popular discrete-time approach based on lifted switched representations. [9][10][11] This work follows a different approach, which is mainly based on state-bounding and the properties of positive systems.…”

Section: Introductionmentioning

confidence: 99%

Delay‐independent conditions of exponential ISS for linear time‐varying delay differential systems

De Iuliis,

Manes

2024

Intl J Robust & Nonlinear

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This work focuses on linear continuous‐time systems with time‐varying delays, in the general case of time‐varying matrices. Initially, we explore the case of positive systems within this class and introduce two distinct delay‐independent conditions of exponential input‐to‐state stability. Moreover, we provide guaranteed exponential convergence rates for such conditions, explicitly stating the ISS gains. Then, we extend our analysis to systems without sign constraints, adopting a state‐bounding approach that takes advantage of the properties of positive systems. Due to the time‐varying nature of the systems, all proposed conditions are in terms of an infinite number of inequalities. Hence, implementation issues are discussed and significant special cases in which the conditions can be cast into a linear programming problem of finite dimension are presented.

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