Robust PWA control Based on State Space Partitions

Based on a convex lifting approach for the state partitions, the present paper studies the sensitivity of piecewise affine (PWA) control laws for linear discrete-time systems with state and input constraints. In particular, the goal is to study the impact of perturbations on the state space partitions. Unlike the current results, which concentrate on the local disturbance of vertex or hyperplane representations, each state partition in this work is considered to be potentially affected. The aim is to characterize the admissible perturbation. Practically, a collection of maximal admissible regions (CMAR) is defined to characterize the maximum perturbation for each set within the original state partition. Based on CMAR, which guarantees the positive invariance of the original controller, and using the induced fragility margin for the associated convex lifting (FMCL) is proposed to realize a PWA control in an implicit (region-free) form. A numerical example illustrates the effectiveness of the new PWA controller.