Robust Controlled Invariant Subspaces and Disturbance Decoupling for Uncertain Switched Linear System

In this paper, we will first study two robust controlled invariant subspaces under common input for a family of vertex systems and for a family of subsystems. Next, disturbance decoupling problems under arbitrary switching via state feedback for polytopic uncertain switched linear systems are formulated, and necessary and sufficient conditions for the problems to be solvable are presented. Further, the disturbance decoupling problems with exponential stability under arbitrary switching are also formulated, and solvability conditions for the problems are briefly discussed. Finally, a numerical example is also investigated.