A Novel Approach to Robust Stability Analysis of Linear Time-Delay Systems∗∗The authors acknowledge Saint Petersburg State University for the research grant 9.37.157.2014.

Medvedeva, Irina V.; Zhabko, Alexey P.

doi:10.1016/j.ifacol.2015.09.383

Cited by 14 publications

(5 citation statements)

References 13 publications

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“…In this section, we present robust stability bounds for Problems 1 and 2. We apply the novel approach 14,15,19 where a simple Lyapunov-Krasovskii functional with derivative (5) is used, and the integral bound for the derivative of the functional along the solutions of the uncertain system is constructed. Let us define the following constants:…”

Section: Robust Stability Conditionsmentioning

confidence: 99%

“…F I G U R E 2 Stability region for system (14) [Colour figure can be viewed at wileyonlinelibrary.com] Example 2. Consider the delay linear distributed system 25…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…We take the nominal pair of parameters (h, a 0 ) = (1, − 0.5) in the stability region of system (14) depicted in Figure 2. The iterative application of Theorem 1, for = 10 −4 , and after 100 iterations, provides the upper bound Δ 0 ≤ 0.2499, whereas that from the exact stability region is Δ 0 < 0.25.…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…In this section, we present robust stability bounds for Problems 1 and 2. We apply the novel approach 14,15,19 where a simple Lyapunov‐Krasovskii functional with derivative (5) is used, and the integral bound for the derivative of the functional along the solutions of the uncertain system is constructed. Let us define the following constants:

\begin{align} M & = \max_{τ \in false[0, h false]} ‖ U false(τ false) ‖, K = true \sum_{k = 0}^{m} ‖ A_{k} ‖, g_{j} = \max_{θ \in false[prefix- h_{j}, 0 false]} ‖ G_{j} false(θ false) ‖, j = \overset{1, m}{true}, β = true \sum_{k = 1}^{m} ‖ A_{k} ‖ h_{k}, γ = true \sum_{k = 1}^{m} g_{k} h_{k}^{2}, \\ α & = 1 + β + γ, P = ρ_{0} + true \sum_{k = 1}^{m} (ρ_{k} + {\overset{ρ}{true}}_{k} h_{k}), N = true \sum_{k = 0}^{m} ‖ A_{k} ‖ false| η_{k} false|, λ = true \sum_{j = 1}^{m} g_{j} false| η_{j} false|, \end{align}

…”

Section: Robust Stability Conditionsmentioning

confidence: 99%

“…It was recently shown that the completeness of the functional is not such a critical issue: 13 the functional with simple negative quadratic term in the instantaneous state has demonstrated to be appropriate for finding matrix 14 and delay 15 uncertainties bounds for linear systems with multiple concentrated delays, giving rise to stability conditions in terms of the Lyapunov matrix of the nominal delay system that are simpler than those obtained by complete type functionals.…”

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confidence: 99%

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Robust stability analysis for linear systems with distributed delays: A time‐domain approach

Juárez

Аlexandrova

Mondié

2020

Intl J Robust & Nonlinear

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This work is devoted to the robust stability analysis of linear systems with distributed delays. The approach is based on recent results in the Lyapunov-Krasovskii framework, where a Lyapunov-Krasovskii functional with prescribed negative definite derivative is applied. The stability conditions obtained in this work, are simple inequalities which depend on the so-called delay Lyapunov matrix. The cases of matrix parameters and delays uncertainties are addressed, accurately detecting exact stability bounds when applied in an iterative manner. Our method is used successfully to tackle the challenging problem of robust predictor-based stabilization of systems with state and input delays.

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Section: Robust Stability Conditionsmentioning

confidence: 99%

“…F I G U R E 2 Stability region for system (14) [Colour figure can be viewed at wileyonlinelibrary.com] Example 2. Consider the delay linear distributed system 25…”

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Illustrative Examplesmentioning

confidence: 99%

\begin{align} M & = \max_{τ \in false[0, h false]} ‖ U false(τ false) ‖, K = true \sum_{k = 0}^{m} ‖ A_{k} ‖, g_{j} = \max_{θ \in false[prefix- h_{j}, 0 false]} ‖ G_{j} false(θ false) ‖, j = \overset{1, m}{true}, β = true \sum_{k = 1}^{m} ‖ A_{k} ‖ h_{k}, γ = true \sum_{k = 1}^{m} g_{k} h_{k}^{2}, \\ α & = 1 + β + γ, P = ρ_{0} + true \sum_{k = 1}^{m} (ρ_{k} + {\overset{ρ}{true}}_{k} h_{k}), N = true \sum_{k = 0}^{m} ‖ A_{k} ‖ false| η_{k} false|, λ = true \sum_{j = 1}^{m} g_{j} false| η_{j} false|, \end{align}

…”

Section: Robust Stability Conditionsmentioning

confidence: 99%

mentioning

confidence: 99%

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Robust stability analysis for linear systems with distributed delays: A time‐domain approach

Juárez

Аlexandrova

Mondié

2020

Intl J Robust & Nonlinear

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Vladimir Kharitonov: Achievements in research

Egorov

2022

Intl J Robust & Nonlinear

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A survey of the main research results of Professor Kharitonov is provided. The following topics are considered: stability analysis of interval polynomials, quasi‐polynomials, and multivariate polynomials; Kalman's hypothesis on the generalization of the Lyapunov matrix equation; critical delay values, complete type functionals and prediction‐based control for time‐delay systems. The fundamentals of Kharitonov's work and the influence of his results on other researchers are discussed.

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New robustness bounds for neutral type delay systems via functionals with prescribed derivative

Аlexandrova

2018

Applied Mathematics Letters

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A Novel Approach to Robust Stability Analysis of Linear Time-Delay Systems∗∗The authors acknowledge Saint Petersburg State University for the research grant 9.37.157.2014.

Cited by 14 publications

References 13 publications

Robust stability analysis for linear systems with distributed delays: A time‐domain approach

Robust stability analysis for linear systems with distributed delays: A time‐domain approach

Vladimir Kharitonov: Achievements in research

New robustness bounds for neutral type delay systems via functionals with prescribed derivative

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