Robust decentralized H-infinity control of multi-channel systems with norm-bounded parametric uncertainties

This paper considers a robust decentralized H-infinity control problem for uncertain multi-channel systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. Our interest is focused on dynamic output feedback. A necessary and sufficient condition for the uncertain multi-channel system to be robustly stabilizable with a specified disturbance attenuation level is developed based on the bounded real lemma, which is reduced to a feasibility problem for a nonlinear matrix inequality (NMI). A two-stage homotopy method is introduced to solve the NMI iteratively. First, a decentralized controller for the nominal system with no uncertainty is computed by imposing structural constraints on the coefficient matrices gradually. Then, the decentralized controller is modified again gradually to cope with the uncertainties.