Input-Output Finite-Time Stabilization of Linear Time-Varying Discrete-Time Systems

This work deals with the Input-Output Finite-Time Stability (IO-FTS) of linear discrete-time systems. In current control science, discrete-time systems play a very important role in many engineering contexts. Moreover, many discrete-time control problems are defined over a finite interval of time, therefore the development and application of finite-time control methodologies is of particular relevance. The first contribution of the paper is a pair of necessary and sufficient conditions for IO-FTS. The former involves the solution of a set of Generalized Difference Lya-punov Equations (GDLEs); the latter allows one to establish the feasibility of an optimization problem by solving a set of Difference Linear Matrix Inequalities (DLMIs). The second contribution of the paper is a theorem for IO finite-time stabilization via state feedback, followed by a more general one for stabilization via output feedback. Both conditions are necessary and sufficient, and lead to optimization problems cast in the form of DLMIs. The applicability of the devised results is illustrated through a numerical example.