Stability analysis of time-varying delay systems based on an improved integral inequalityinequalities
The delay-dependent stability problem of a class of linear systems with time-varying delay is studied.An improved Composite Slack-Matrix-Based Integral Inequality(CSMBII)is presented.It overcomes the restriction of mutual convexity in Bessel-Legendre integral inequalities and makes CSMBII more convenient to deal with time-varying delay systems.To some extent,it overcomes the disadvantage that relaxation matrix is independent of time-varying delay in previous work.On the basis of Based on CSMBII,a Lyapunov-Krasovskii(L-K)functional with double integral form is constructed by using Lyapunov stability theory,and a new delay-dependent stability criterion is derived.Two numerical examples are given to illustrate the validity of the stability criterion.
Time-varying delay systemLyapunov-Krasovskii functionalComposite slack-matrix-based integral inequality(CSMBII)Stability criterion
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