Disturbance decoupling with stability in discrete-time switching linear systems: Arbitrary switching

The problem of disturbance decoupling with stability consists in finding a compensator that renders the output of a dynamical system insensitive to undesired inputs, while assuring stability, in a suitable sense, of the compensated dynamics. Disturbance decoupling is a classic problem in control theory as well as a primary concern in control system design. This work deals with disturbance decoupling in discrete-time switching linear systems subject to arbitrary switching. Inaccessible and measurable disturbances are considered in a unified setting. Different problem formulations are investigated, with progressively more severe stability requirements: namely, the study starts from structural decoupling and ends to decoupling with input-to-state stability. Solvability conditions for the stated problems are proven. In particular, necessary conditions for stabilization of the inner and outer switching dynamics of the resolving subspace are shown. A convex procedure for the computation of the switching state feedback which simultaneously achieves disturbance decoupling and closed-loop stability is presented. The proposed methodology is illustrated through a worked out numerical example.