An improved summation inequality to discrete-time systems with time-varying delay.

*(English)*Zbl 1348.93185Summary: The summation inequality plays an important role in developing delay-dependent criteria for discrete-time systems with time-varying delay. This note proposes an improved summation inequality to estimate the summation terms appearing in the forward difference of Lyapunov-Krasovskii functional. Compared with the inequality recently developed by the Wirtinger-based summation inequality and the reciprocally convex lemma, the proposed one reduces the estimation gap while requires the same number of decision variables. A relaxed stability criterion of a linear discrete-time system with a time-varying delay is established by using such novel inequality. Two numerical examples are given to demonstrate the advantages of the proposed method.

##### MSC:

93C55 | Discrete-time control/observation systems |

93C05 | Linear systems in control theory |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

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