Exponential estimates for solutions of linear systems with distributed delay

Medvedeva, Irina V.

doi:10.1109/scp.2015.7342124

Cited by 1 publication

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…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%

See 1 more Smart Citation

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

Juárez

Аlexandrova

Mondié

2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

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.

show abstract

Section: Robust Stability Conditionsmentioning

confidence: 99%