Robust Finite-Time Stabilization via Dynamic Output Feedback: An LMI Approach

In this paper we consider the finite-time stabilization problem for a linear system subject to parametric time-varying uncertainties. The main result of this work is a sufficient condition for the design of a dynamic gain scheduled output feedback controller which renders the closed loop system finite-time stable for all possible time realizations of the parameters. Such sufficient condition is given in terms of an LMI optimization problem; this gives the opportunity of fitting the finite-time control problem in the general framework of the LMI approach to the multiobjective synthesis. In this context an example illustrates the design of a controller which guarantees, at the same time, finite-time specifications and some pole placement requirements.