Journal ArticleDOI
An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay
Reads0
Chats0
TLDR
An extended reciprocally convex matrix inequality is developed, which reduces the estimation gap of the R CCL-based matrix inequality and reduces the number of decision variables of the recently proposed delay-dependent RCCL.About:
This article is published in Automatica.The article was published on 2017-11-01. It has received 314 citations till now. The article focuses on the topics: Linear matrix inequality & Convex combination.read more
Citations
More filters
Journal ArticleDOI
Stability of Linear Systems With Time-Varying Delays Using Bessel–Legendre Inequalities
TL;DR: This paper addresses the stability problem of linear systems with a time-varying delay by taking advantages of the dependence of the stability criteria on both the delay and its derivative to propose a new definition of allowable delay sets.
Journal ArticleDOI
A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems
TL;DR: A generalized free-matrix-based integral inequality (GFMBII) is presented that overcomes the drawback that the Bessel–Legendre inequality is inconvenient to cope with a time-varying delay system as the resultant bound contains a reciprocal convexity.
Journal ArticleDOI
A relaxed quadratic function negative-determination lemma and its application to time-delay systems
TL;DR: A parameter-adjustable-based lemma is developed, which contains the lemma popularly used in literature as a special case and has potential to reduce the conservatism without requiring extra decision variables.
Journal ArticleDOI
Generalized reciprocally convex combination lemmas and its application to time-delay systems
TL;DR: It is proved that these existing inequalities can be captured as particular cases of Moon et al.'s inequality and found strong links not only with the most recent and efficient matrix inequalities such as the reciprocally convex combination lemma and also its relaxed version but also with some previous inequalities.
Journal ArticleDOI
Lyapunov conditions for finite-time stability of time-varying time-delay systems
Xiaodi Li,Xueyan Yang,Shiji Song +2 more
TL;DR: The efficiency of the proposed criteria is illustrated by three numerical examples, where a stabilizing memoryless controller for FTCS of a second-order LTV system with time delay is proposed.
References
More filters
Journal ArticleDOI
Reciprocally convex approach to stability of systems with time-varying delays
TL;DR: This paper suggests the lower bound lemma for such a combination, which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables, comparable to thosebased on the Jensen inequalityLemma.
Journal ArticleDOI
Wirtinger-based integral inequality: Application to time-delay systems
TL;DR: An alternative inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities is proposed and it is shown that this resulting inequality encompasses the Jensen one and also leads to tractable LMI conditions.
Proceedings ArticleDOI
An integral inequality in the stability problem of time-delay systems
TL;DR: In this paper, an integral inequality is derived, and applied to the stability problem of time-delay systems using discretized Lyapunov functional formulation, and a simpler stability criterion is derived.
Journal ArticleDOI
Technical Communique: Delay-dependent criteria for robust stability of time-varying delay systems
TL;DR: Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account, which are less conservative than existing ones.
Journal ArticleDOI
Technical communique: Delay-range-dependent stability for systems with time-varying delay
TL;DR: The present results may improve the existing ones due to a method to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed Lyap unov functional, which take into account the range of delay.