Disturbance Decoupling via State Feedback for Uncertain Switched Linear Systems

In this paper disturbance decoupling problems via state feedback for polytopic uncertain switched linear systems under arbitrary switching are studied in the framework of the so-called geometric control theory. Firstly, robust controlled invariant subspaces under common input for a family of vertex systems are studied. After that disturbance decoupling problem under arbitrary switching is formulated, and then a necessary and sufficient condition for the problem to be solvable is presented. Further, the disturbance decoupling problem with quadratic stability is also formulated, and sufficient conditions for the problem to be solvable are presented. Finally, an illustrative numerical example is given.