Design of robust H∞ control for interconnected systems:: A homotopy method

This paper considers a robust decentralized H. control problem for uncertain large-scale interconnected systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist In subsystems. A design method based on the bounded real lemma is developed for a dynamic output feedback controller, which is reduced to a feasibility problem for a nonlinear matrix inequality (NMI). It is proposed to solve the NMI iteratively by the idea of homotopy, where some of the variables are fixed alternately on each iteration to reduce the NMI to a linear matrix inequality (LMI). A decentralized controller for the nominal system is computed first by imposing structural constraints on the coefficient matrices gradually. Then, the decentralized controller is modified again gradually to cope with the uncertainties. A given example shows the efficiency of this method.