Stabilization of switched linear systems by using projections

摘要

This paper proposes a new approach to stabilize switched linear systems. In this method, the projections are employed to establish the stabilization of a switched systems class. Hence, we suppose that the subsystems given by a switched linear system can be projected to the same subspace. Under these conditions, we prove that this switched linear system is stabilizable if and only if a low-order switched linear system is also stabilizable. In order to complete this study, we present a counter example that proves that it is not always possible to use the projections. Moreover, the main result in the paper is applied to solve the stabilization of a third-order switched systems class and the static feedback stabilization of a switched linear systems class. Finally, a numerical example is included in order to illustrate the new method obtained to stabilize a third-order switched systems class.