Discrete-time switched systems: pole location and structural constrained control

This paper addresses the problem of state feedback control of discrete-time switched systems with linear modes of operation. Sufficient linear matrix inequality conditions are given for the existence of a state feedback control law assuring: i) pole location inside a circle for each linear mode of operation; ii) overall stability for any arbitrarily fast switching sequence. Two feedback control laws are investigated: the first one with a fixed gain for all linear modes and the second using a switched gain. Moreover, structural constraints such as decentralization can be easily imposed to the feedback gains. Simulation results show that with the switched gain more stringent design specifications can be imposed to the closed-loop system, providing closed-loop performances that cannot be produced by means of a constant feedback gain.