Bounded realness for discrete-time jump descriptor systems

Abstract

In this paper, we propose a new bounded real lemma (BRL) for discrete-time jump descriptor systems (DJDSs). While the existing studies consider the sufficient condition for the BRL of DJDSs, this paper successfully suggests the necessary and sufficient condition for the BRL of DJDSs. To hold the necessity and sufficiency in terms of linear matrix inequality, two slack variables are introduced by coupling the variables and matrix in the null-space of the singular matrix in DJDSs. A numerical example is provided to show the validity of the result.