Robust decentralized H_∞ control for interconnected descriptor systems with norm-bounded uncertainties

This paper considers a robust decentralized H_∞control problem for interconnected descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and existing in both the system and control input matrices. Our interest is focused on dynamic output feedback. A sufficient condition for an uncertain interconnected descriptor system to be robustly stabilizable H_∞ control with a specified disturbance attenuation level 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 descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is gradually modified from the nominal descriptor system (without uncertainties) to the original system with 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.