Robust decentralized H∞ control for multi-channel continuous-time systems with time-delays

This paper considers a robust decentralized H_infin control problem for multi-channel continuous-time systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in the system, delay and control input matrices. Our interest is focused on dynamic output feedback. A sufficient condition for an uncertain multi-channel continuous-time delay system to be robustly stabilizable with H_infin norm is derived in terms of a nonlinear matrix inequality (NMI). A two-stage homotopy method is employed to solve the NMI iteratively. First, a decentralized controller for the nominal continuous-time delay system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the usefulness of this method.