Finite-Time Stabilization of Linear Time-Varying Continuous Systems

In this technical note, the problem of finite time stabilization of linear time-varying continuous systems is considered. Necessary and sufficient conditions, based upon the solution to some Lyapunov differential matrix equations, are proposed for particular cases of interest. From these conditions, the design of time-varying state feedback controller guaranteeing the finite time closed-loop stability is presented. Numerical experiments illustrate the potentialities of the approach.

I. Introduction

In control theory, the concept of Lyapunov stability is very popular, particularly when dealing with systems described in the state space [1]. Numerous applications in both control design or analysis problems contexts are widely based on the concept of Lyapunov stability because it corresponds in general to a satisfactory behavior in practice, even if from a performance point of view, other constraints have to be imposed.