Positive Finite Time Stabilization for Discrete Time Linear Systems

Abstract

In this paper, a new finitetime stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discretetime linear systems. Differently from previous FTSrelated papers, the initial state as well as the state trajectory is required to be in the nonnegative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closedloop system is positively finitetime stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of nonnegativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.