Invariant Sets for Switched Discrete Time Systems subject to Bounded Disturbances

Authors:	Grieder Pascal, ETH Zurich, Switzerland Rakovic S.V., Imperial College London, United Kingdom Morari M., ETH Zurich, Switzerland Mayne D.Q., Imperial College London, United Kingdom
Topic:	1.3 Discrete Event and Hybrid Systems
Session:	Switched Dynamic Systems I
Keywords:	switched systems, robust invariant sets, minimum time control

Abstract

This paper addresses invariant set computation for discrete-time switched systems subject to bounded disturbances. Specifically, we show how to compute the maximal robustly switched invariant set, which we define to be the set of states which can be made robustly invariant by an appropriate switching law. Furthermore it is demonstrated how the maximal robustly reachable set can be computed, i.e., all states which can be robustly steered into the target set by an appropriate switching law. We also show how these sets may be used to obtain a minimum time controller for switched systems, i.e., a controller which robustly steers the state into a given target set in minimal time.