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Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems. (English) Zbl 1330.93213
Summary: This paper is concerned with stability of linear discrete time-delay systems. Note that a tighter estimation on a finite-sum term appearing in the forward difference of some Lyapunov functional leads to a less conservative delay-dependent stability criterion. By using Abel lemma, a novel finite-sum inequality is established, which can provide a tighter estimation than the ones in the literature for the finite-sum term. Applying this Abel lemma-based finite-sum inequality, a stability criterion for linear discrete time-delay systems is derived. It is shown through numerical examples that the stability criterion can provide a larger admissible maximum upper bound than stability criteria using a Jensen-type inequality approach and a free-weighting matrix approach.

93D99 Stability of control systems
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
Full Text: DOI
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