This note proposes a systematic method to optimizing dynamic output feedback controller for continuous-time hybrid systems in the Piecewise Affine (PWA) form. In this note, design of the dynamic output feedback controller is shown in the frame of L2 gain synthesis for PWA systems. Matrix inequalities derived from dynamic output feedback controller is not usually linear. Using a congruence transformation, the nonlinear matrix inequalities are mapped into linear matrix inequalities, whose solutions are quite feasible using commercially available software. The proposed techniques satisfy features such as: globally quadratic stability, continuity of control signal, and tracking a reference input. A numerical example is included to demonstrate the applicability and effectiveness of the proposed technique.
Piecewise affine output feedback controller for vehicle lane keeping