离散线性时滞系统的指数稳定性分析:基于加权离散正交多项式的方法

摘要

研究离散线性时滞系统的指数稳定性分析问题.引入离散内积,用Gram-Schmidt正交化方法,提出加权离散正交多项式(WDOPs),推出基于WDOPs的求和不等式,包括离散Jensen不等式和离散Writinger-型作为特殊情形;利用基于WDOPs的求和不等式,建立离散线性时滞系统的指数稳定性判据.数值实例说明了结果的有效性.%The problem of exponential stability analysis of linear delayed discrete-time systems is investigated.Weighted discrete orthogonal polynomials (WDOPs) are proposed by introducing a discrete inner product and utilizing the Gram-Schmidt orthogonalization method.From which,the WDOPs-based summation inequalities,including discrete Jensen inequality and discrete Writinger-type inequality as special cases,are derived.The WDOPs-based summation inequalities are applied to establish exponential stability criterion for linear delayed discrete-time systems.The obtained theoretical results are illustrated by a numerical example.