FTS of Discrete-Time Linear Systems

In this chapter, we deal with some finite-time control problems for discrete-time linear time-varying (DT-LTV) systems. First, we provide necessary and sufficient conditions for finite-time stability; such conditions can be regarded as the discrete-time counterparts of the results stated in Theorem 2.1. Indeed, one condition involves the computation of the state transition matrix; the other condition requires the solvability of a difference Lyapunov equality (DLE) or the feasibility of a difference linear matrix inequality (DLMI), respectively. The DLMI condition is the basis for the solution of the state and output feedback problems, which, again, are expressed in terms of optimization problems involving DLMIs.