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（英文）

Exponential stability analysis of linear delayed discrete-time systems: a weighted discrete orthogonal polynomials-based approach

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 investi- gated. 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 sum- mation 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 stabili- ty criterion for linear delayed discrete-time systems. The obtained theoretical results are illustrated by a numerical example.