Finite-time control of discrete-time linear systems: Analysis and design conditions

In this paper we deal with some finite-time control problems for discrete-time, time-varying linear systems. First we provide necessary and sufficient conditions for finite-time stability; these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference Lyapunov inequality. Then we address the design problem. The proposed conditions allow us to find output feedback controllers which stabilize the closed loop system in the finite-time sense; all these conditions can be expressed in terms of LMIs and therefore are numerically tractable, as shown in the example included in the paper.