Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems.

*(English)*Zbl 1330.93213Summary: 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.

##### MSC:

93D99 | Stability of control systems |

93C05 | Linear systems in control theory |

93C55 | Discrete-time control/observation systems |

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\textit{X.-M. Zhang} and \textit{Q.-L. Han}, Automatica 57, 199--202 (2015; Zbl 1330.93213)

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