Disturbance decoupling of switched linear systems

Abstract

In this paper, we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version, the exogenous input is considered as the disturbance, in the second, the switching signal and in the third both of them are considered as disturbances. All three versions of disturbance decoupling have direct counterparts for linear parameter-varying (LPV) systems, while the latter instance of the problem is relevant for disturbance decoupling of piecewise linear systems, as we will show. The solutions of the three disturbance decoupling problems will be based on geometric control theory for switched linear systems and will entail both mode-dependent and mode-independent static state feedback.