Abstract
This paper considers a robust decentralized H∞ 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 derived based on the bounded real lemma, which is reduced to a feasibility problem 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 system with no uncertainty is computed by imposing structural 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, a variable is fixed alternately at the iterations to reduce the NMI to a linear matrix inequality (LMI). A given example shows the efficiency of this method.
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