Improved linear matrix inequality approach to stability analysis of linear systems with interval time-varying delays

Abstract

Please cite this article as: A. Farnam, R. Mahboobi Esfanjani, Improved linear matrix inequality approach to stability analysis of linear systems with interval time-varying delays, Journal of Computational and Applied Mathematics (2015), http://dx.Abstract -This paper investigates the problem of stability analysis for a class of linear systems with interval time-varying delay. In order to develop a less conservative stability condition, a LyapunovKrasovskii functional comprising novel integral terms is introduced. Convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities (LMIs) without any additional freeweighting matrices which decreases drastically the computational burden of the stability test. Numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature.

Improved delay‐range‐dependent stability analysis for uncertain retarded systems based on affine Wirtinger‐inequality

“…Remark For Example recently authors in obtained τ 2 = 3.6271 for τ 1 = 2 and μ = 0.2, whereas using Theorem , we could obtain τ 2 = 3.82. Subsequently, in it is reported that delay upper bound ( τ 2 ) increases with increase in delay derivative ( μ ) for a given delay lower bound ( τ 1 ) that is erroneous and hence this result is not considered for comparison.…”

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

“…Delay‐dependent case has the advantage of using information on the maximal size of the delay bound , and hence, it yields less conservative result over the delay‐independent case . For the recent progress of time‐delay system, the reader may refer to and the reference therein. Liu et al.…”

“…Delay-dependent case has the advantage of using information on the maximal size of the delay bound [10][11][12], and hence, it yields less conservative result over the delay-independent case [13]. For the recent progress of time-delay system, the reader may refer to [14][15][16][17][18][19][20][21] and the reference therein. Liu et al [22] obtained a delaydependent finite-time stability criterion for a class of nonlinear time-varying delay systems by using fuzzy approach.On the other hand, in most of the practical control systems, component failures such as sensors and actuators are commonly occurring because of the component aging, dead zone, relay effects, and so on.…”

Further Studies on Stability and Stabilization of T‐S Fuzzy Systems With Time‐Varying Delays via Fuzzy Lyapunov‐Krasovskii Functional Method

“…Recently, on the basis of the Jensen inequality, the Wirtinger‐based integral inequality was proposed in to reduce the conservative property of the Jensen inequality, and has already attracted significant attention . Furthermore, triple and quadruple integral terms were incorporated in and to improve the stability condition, but the forms of LKF were simple.…”