Stabilization of uncertain switched symmetric composite systems

Complexity-reduced design of a decentralized H∞ state switching controller is presented for nonlinear but nominally linear uncertain continuous-time switching symmetric composite systems with a state-dependent switching rule. First, a reduced-order control design system and an associated non-switching uncertain combination linear system are constructed. Then, the robust H∞ control via switched state feedback is designed for the design system using a min-projection strategy. Finally, it is proved that if this low-order switching controller and the state-dependent switching rule are used as identical switching local controllers of a decentralized switching controller for the global system, then the controller renders the global closed-loop system quadratically stable with prescribed disturbance attenuation bound. The switching decentralized rules depend only on local subsystems states.