A procedure for simultaneously stabilizing a collection of single input linear systems using non-linear state feedback control

Abstract

This paper considers the problem of simultaneously stabilizing a finite collection of single input linear systems. This stabilization is achieved using a single non-linear state feedback controller. The stability of the resulting closed loop system is established using a collection of quadratic Lyapunov functions. The main result of this paper is a sufficient condition for simultaneous stabilizability. Furthermore, when this sufficient condition is satisfied, the paper gives a formula for constructing the stabilizing feedback control law. The paper includes an example in which the stabilization procedure is applied to the stabilization of an F4E fighter aircraft. Show more