Set-membership state estimation for delayed switched systems with interval uncertainty: A zonotopic approach

Considering the existence of time delay and interval uncertainty, a set-membership state estimation problem based on zonotopes is studied for discrete-time switched systems subject to unknown but bounded noises. To conform the actual situation, a state observer asynchronous with the subsystem is designed. The $L_{\infty }$ performance is introduced to attenuate the effect of noises in the observer design. By dealing with the interval uncertainty, the design approach of $L_{\infty }$ observer is given and transformed into a convex optimization problem which can be solved off-line. The zonotope and the estimation interval containing state are provided based on the $L_{\infty }$ observer. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.