Growth Conditions for Global Exponential Stability and Exp-Iss of Time-Delay Systems Under Point-Wise Dissipation

Karafyllis, Iasson; Pepe, Pierdomenico; Wang, Yuan; Chaillet, Antoine

doi:10.2139/ssrn.4108415

Cited by 4 publications

(9 citation statements)

References 28 publications

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“…Although not explicitly remarked for all results of Sections 3 and 4, exp-ISS with linear gains (see Def. 2 of Chaillet et al 38 ) can be specifically stated for Theorems 2,4,6,7.…”

Section: Theorem 7 Consider System (1) With B(t) and U(t) Satisfyingmentioning

confidence: 93%

“…The definition of exp-ISS with linear gains is reported in Def. 2 of Chaillet et al 38 The terminology "delay-independent" stability will be used to mean that the stability of (1) holds robustly against bounded time-varying delays of any magnitude, that is, for any 𝛿 j (t) ∈ [0, 𝛿] and any given 𝛿 ∈ R + , j = 1, … , r.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…starting from a nonnegative initialization 𝜂 t = 𝜁 t − 𝜁 t . As a consequence the solution 𝜂(t) remains nonnegative for all t ≥ t. Now, consider system (38) such that at a given time t the state 𝜁 t is as follows…”

Section: Theorem 2 Consider System (1) Under the Same Positivity Cond...mentioning

confidence: 99%

“…which is nonnegative thanks to the property (31). Then, after replacing 𝜈(t) into (38), we get that the solution 𝜁(t) obeys the following differential equation…”

Section: Theorem 2 Consider System (1) Under the Same Positivity Cond...mentioning

confidence: 99%

See 3 more Smart Citations

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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“…Although not explicitly remarked for all results of Sections 3 and 4, exp-ISS with linear gains (see Def. 2 of Chaillet et al 38 ) can be specifically stated for Theorems 2,4,6,7.…”

Section: Theorem 7 Consider System (1) With B(t) and U(t) Satisfyingmentioning

confidence: 93%

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Theorem 2 Consider System (1) Under the Same Positivity Cond...mentioning

confidence: 99%

“…which is nonnegative thanks to the property (31). Then, after replacing 𝜈(t) into (38), we get that the solution 𝜁(t) obeys the following differential equation…”

Section: Theorem 2 Consider System (1) Under the Same Positivity Cond...mentioning

confidence: 99%

See 2 more Smart Citations

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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“…Halanay's result then asserts that the Lyapunov function decays exponentially along solutions, provided that the gain of the negative term is greater than that of the positive term, which can then be used to derive GAS or GES depending on the function's properties [Baker and Buckwar, 2005, Bresch-Pietri et al, 2012, Fridman, 2014, Pepe and Fridman, 2017, Katz and Fridman, 2022. It was recently shown that the gains can also be picked nonlinear, provided that their difference is a positive definite unbounded function [Pepe, 2022]. The Razumikhin and Halanay methods share a lot in common: they both rely on a Lyapunov function and both treat delayed terms as disturbances that tend to act against stability.…”

Section: Introductionmentioning

confidence: 99%

Building coercive Lyapunov–Krasovskii functionals based on Razumikhin and Halanay approaches

Loko,

Chaillet,

Karafyllis

2024

Intl J Robust & Nonlinear

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In this article, we provide a systematic and constructive way to build a Lyapunov–Krasovskii functional for time‐delay systems whose stability can be established through the Razumikhin or the Halanay approaches. The constructed Lyapunov–Krasovskii functional turns out to be coercive, meaning sandwiched between functions of the state history norm, and to dissipate in terms of the whole history norm. We present these results in the framework of input‐to‐state stability (ISS) in order to further account for the influence of input disturbances. A special emphasis is also given on exponential stability and exponential ISS. We illustrate our findings though the study of a coupled ODE‐PDE model of a chemical reactor, and show that, unlike most results in that area, our approach happens to ensure ISS in terms of the supremum norm of the state.

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The ISS framework for time-delay systems: a survey

Chaillet

Karafyllis

Pepe

et al. 2023

Math. Control Signals Syst.

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At the occasion of Eduardo D. Sontag's 70 th birthday, we provide here an overview of the tools available to study input-to-state stability (ISS) and related notions for time-delay systems. After a hopefully pedagogical presentation of the main differences with respect to the finite-dimensional theory, we review basic stability concepts for input-free time-delay systems, as well as instruments to guarantee them in practice, including the Lyapunov-Krasosvkii, Lyapunov-Razumikhin, and Halanay approaches. We then consider the influence of inputs through the notions of ISS, integral ISS, and input-to-output stability and provide both Lyapunov-like and solutions-based characterizations of these properties. We also show how these notions can be helpful for the stability analysis of interconnected systems, whether in cascade or in feedback form. We finally provide a list of questions which remain open until now.

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Growth Conditions for Global Exponential Stability and Exp-Iss of Time-Delay Systems Under Point-Wise Dissipation

Cited by 4 publications

References 28 publications

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

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

Building coercive Lyapunov–Krasovskii functionals based on Razumikhin and Halanay approaches

The ISS framework for time-delay systems: a survey

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