Attainability and set analysis for uncertain PWA systems with parameter variations and bounded disturbance

This paper considers discrete-time, uncertain piecewise affine (PWA) systems affected by both parameter variations and bounded disturbances. We are interested in the characterization of attainability, understood as the reachability of a state space region, associated to a certain invariance property. Our approach computes in the first stage the maximal set in the state space from which states can be driven to the target region while taking into account the system uncertainties. A polyhedral approach to find the minimum safety horizon (cyclic invariance set) to maintain the system states within the given target region is then presented. A new polyhedral algorithm is proposed to reduce the number of polyhedral regions and decrease the required memory size and consequently the robust control computation load.