Interconnected switched discrete-time systems: robust stability and stabilization

This paper develops a decentralized approach to the robust stability and stabilization problems of class of non-linear interconnected discrete-time systems with arbitrary switched rules. This class of interconnected systems consists of coupled nominally linear subsystems with unknown-but-bounded state delay. We showed that multi-controller switched schemes provide an effective and powerful mechanism to cope with highly complex systems with large uncertainties. We developed a delay-dependent decentralized structure that guarantees asymptotic stability with local disturbance attenuation on the subsystem level. Then we constructed decentralized switched control schemes based on state feedback and dynamic output feedback to ensure stabilizability of the global system with ℓ2-performance bound. The theoretical developments are demonstrated by numerical simulation of a multi-reach water pollution control problem.