Verifying asymptotic bounds for discrete-time sliding mode systems with disturbance inputs

This work presents a procedure for verifying asymptotic bounds on the behaviors of a class of discrete-time hybrid systems with disturbance inputs. First, an invariant set satisfying the given asymptotic bounds is computed. Then, conservative approximations of the reachable sets starting from the set of initial states are computed until the target invariant set is reached. Both steps in the procedure use LMI-based algorithms for computing minimal-volume ellipsoidal approximations to the actual reachable sets. The methods are particularly useful for analyzing the asymptotic behaviors of discrete-time sliding mode systems. The approach is illustrated for two examples.