LQ optimal control for a class of hybrid systems

This paper deals with the problem of computing a state feedback optimizing a quadratic cost function for a class of linear hybrid systems. A solution to the finite-horizon and infinite-horizon Linear Quadratic optimal control problem is found through an hybrid extension of classical Differential and Difference Riccati Equations. Necessary and sufficient conditions, guaranteeing that the infinite-horizon optimal control stabilizes the closed loop system, are stated. A physically motivated example is reported.