Set-membership state estimation for discrete time piecewise affine systems using zonotopes

This paper presents a method for guaranteed state estimation of discrete time piecewise affine systems with unknown but bounded noise and disturbance. Using zonotopic set representations, the proposed method computes the set of states that are consistent with the model, observation, and bounds on the noise and disturbance such that the real state of the system is guaranteed to lie in this set. Because in piecewise affine systems, the state space is partitioned into a number of polyhedral sets, at each iteration the intersection of the zonotopes containing a set-valued estimation of the states with each of the polyhedral partitions must be computed. We use an analytic method to compute the intersection as a zonotope and minimize the size of the intersection. A numerical example is provided to illuminate the algorithm.