Integration of real-time and stability constraints via hybrid polytopic partitions

This paper investigates the integration of control theory and real-time implementation specifications within a single tractable controller synthesis method. It is proposed to guarantee real-time feasibility through specific low-complexity partitions of the piecewise affine (PWA) control law. The control-theory specification, i.e., stability under state and input constraints, are integrated through conic partitions induced by a polyhedral control Lyapunov function (CLF). The combination of the controller and conic partitions yields the hybrid polytopic partition, which is the cornerstone of the developed synthesis method. Based on the HPP, the controller synthesis is pursued by low complexity linear programming. The effectiveness of the approach is demonstrated in a case-study on real-time control of a buck power converter.