Low-complexity stabilizing PWA controllers for linear systems with parametric uncertainties

Abstract

Explicit MPC often results in a large number of irregular partitions in the feasible region as the dimension of the system increases and the storage requirement for the control and region parameters often limit its applications. In this paper, we consider a class of discrete-time linear systems with polytopic parametric uncertainties and provide a robust control Lyapunov based synthesis method to obtain robust low-complexity PWA controllers on regular partitionings. By implementing a refinement procedure, we can fit the PWA feedback control law in each regular partitioning based on feasibility of linear programming problems, which preserves stability, constraint satisfaction, and certain performance requirement. Numerical examples will demonstrate the effectiveness of the approach.