Robust Decentralized H∞ Control for Discrete-Time Systems with Time-Delay Using Homotopy Method

This paper considers a robust decentralized H_∞ control problem for multi-channel discrete-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 multichannel discrete-time delay system to be robustly stabilizable with H_∞ 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 discrete-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). A given example shows the usefulness of this method.