Feedback control design for discrete-time piecewise affine systems

This paper investigates the design of state feedback and dynamic output feedback stabilizing controllers for discrete-time piecewise affine (PWA) systems. The main objective is to derive design methods that incorporate the partition information of the PWA systems so as to reduce the design conservatism embedded in existing design methods. We first introduce a transformation that converts the feedback control design problem into a bilinear matrix inequality (BMI) problem. Then, two iterative algorithms are proposed to compute the feedback controllers characterized by the BMI. Several simulation examples are given to demonstrate the advantages of the proposed design.