Abstract
This paper proposes an improved stability condition of discrete-time systems with variable delays. Based on some mathematical techniques, a series of new summation inequalities are obtained. These new inequalities are less conservative than the Jensen inequality. Based on these new summation inequalities and the reciprocally convex combination inequality, a novel sufficient criterion on asymptotical stability of discrete-time systems with variable delays is obtained by constructing a new Lyapunov-Krasovskii functional. The advantage of the proposed inequality in this paper is demonstrated by a classical example from the literature.
Highlights
Time delay is usually encountered in many practical situations such as signal processing, image processing etc
The problem of the delay-dependent stability analysis of timedelay systems has become a hot research topic in the control community [, ] due to the fact that stability criteria can provide a maximum admissible upper bound of time delay
The maximum admissible upper bound can be regarded as an important index for the conservatism of stability criteria [ – ]
Summary
Time delay is usually encountered in many practical situations such as signal processing, image processing etc. Seuret et al [ ] obtained a new stability criterion for the discrete-time systems with time-varying delay via the following novel summation inequality. Based on the novel inequalities, some new stability criteria are presented for systems with time-varying delays by constructing some appropriate Lyapunov-Krasovskii functionals in [ ]. In order to get less conservative results, Jensen’s integral inequality, Wirtinger’s integral inequality, and a free-matrix-based integral inequality are proposed to obtain a tighter upper bound of the integrals occurring in the time derivative of the Lyapunov-Krasovskii functional. Only a few papers have studied the summation inequalities and their application in stability analysis of discrete-time systems with variable delays. Motivated by the above works, in order to provide a tighter bound for r – j=r (i)Ry(i), this paper is aimed at establishing some novel summation inequalities as the discrete-time versions of the integral inequalities obtained in [ ]. The symbol ∗ within a matrix represents the symmetric term of the matrix
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