Robust Control of Linear Systems via Switching

The standard approach to the problem of controlling linear systems with large parameter uncertainty is to seek a controller that stabilizes the system and achieves a required performance over the whole polytope of uncertainty. In the case where the latter polytope is large, the design may become very conservative. We present an alternative approach where the uncertainty polytope is divided into overlapping smaller regions and where each of these regions is assigned to a separate subsystem. Assuming that there is online information on which of the regions the parameters of the system move to, a recently developed method for
H
_∞
design of switched system with dwell time is applied. A Lyapunov Function (LF) in a quadratic form, which is non-increasing at the switching instants, is assigned to each subsystem. This function is used to determine the stability and to find a bound on the
L
₂
-gain of the switched system. The obtained results are used to solve the corresponding robust
H
_∞
state-feedback and static output-feedback control problems.