Admissible Finite Time Stability and Stabilization of Uncertain Discrete Singular Systems

Abstract

The problems of admissible finitetime stability (AFTS) and admissible finitetime stabilization for a class of uncertain discrete singular systems are addressed in this study. The definition of AFTS is first given. Second, a sufficient condition for the AFTS of the nominal unforced system is established, which is further extended to the uncertain case. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closedloop system is admissibly finitetime stable for all admissible uncertainties. Both the AFTS and the controller design conditions are presented in terms of linear matrix inequalities (LMIs) with a fixed parameter. Finally, two numerical examples are provided to illustrate the effectiveness of the developed theory.