基于DOPs的求和不等式及其在离散线性时滞系统稳定性分析中的应用（英文）

A DOPs-based summation inequality and its application to stability analysis of linear delayed discrete-time systems

引入一个离散内积,应用Gram-Schmidt正交化过程,得到离散正交多项式(DOPs)集,推出一个基于DOPs的求和不等式,该不等式包含一个非负整数N作为参数,N越大,这个不等式越精确。应用此求和不等式,建立一类离散线性时滞系统的稳定性判据。数值例子说明了本方法的有效性,同时给出了与一些现有结果的比较。

By introducing a discrete inner product, a set of discrete orthogonal polynomials （DOPs） is obtained by applying the Gram-Schmidt orthogonalization process. From which, a DOPs-based summation inequality, containing a nonnegative integer N as a parameter, is proven. The larger the parameter N is, the more accurate the DOPs-based summation inequality becomes. The DOPs-based summation inequality is applied to establish stability criterion for a class of linear delayed discrete-time systems. The effective- ness of the proposed approach is illustrated by a numerical example.