A New Stability Criterion for Systems with Distributed Time-Varying Delays via Mixed Inequalities Method

Abstract

This paper is concerned with the delay-dependent stability of systems with distributed time-varying delays. The novelty relies on the use of some new inequalities which are less conservative than some existing inequalities. A less conservative stability criterion is obtained by constructing some new augmented Lyapunov–Krasovskii functionals, which are given in terms of linear matrix inequalities. The effectiveness of the presented criterion is demonstrated by two numerical examples.

Improved Stability Criteria on Linear Systems with Distributed Interval Time-Varying Delays and Nonlinear Perturbations

“…The values in Table 2 are the maximum upper with (53). The values in Table 2 are the maximum upper bounds on the delay h 2 under different values of u than those in [6][7][8]15,22,24,26]. Table 2.…”

“…The stability criteria of dynamical systems with time-varying delays and nonlinear perturbations have received the attention of many theoreticians and engineers in this field over the last few decades [4,9,14,18,25,28]. For delay-dependent stability criteria, the main concern is to enlarge the feasible region of the criteria to guarantee the asymptotic stability of time-delay systems in a given time-delay interval [2,3,6,7,22,23]. A descriptor model transformation and a corresponding Lyapunov-Krasovskii functional were introduced for the stability analysis of systems with delays in [19,21].…”

“…where η and ρ are known real positive constants. More recently, the authors studied the problem of stability analysis for linear systems with distributed time-varying delays in [22] in the form:…”