Robust Control of Linear Systems via Switching

An alternative approach to robust control is presented 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 an online information on which of the regions the parameters of the system move to, the method of the previous chapters for H_∞ design of switched system with dwell time is applied. In order to handle the switching between the subsystems, a Lyapunov Function (LF) in a quadratic form, which is nonincreasing at the switching instances, is assigned to each subsystem. This function is used to determine the stability and to find a bound on the L₂ -gain of the switched system. The obtained results are then used to solve the corresponding robust H_∞ state-feedback and static output-feedback control problems. Two practical examples are given which show that, by deliberately introducing switching, the obtained designs are less conservative than those achieved by the available standard techniques.