Abstract
This paper considers a decentralized mixed H2/H∞ control problem for uncertain interconnected systems. The uncertainties are assumed to be value-bounded, and exist in system, control input and interconnection matrix of subsystems. A nonlinear matrix inequality (NMI) condition is derived for a robust decentralized H2/H∞ controller to exist, which achieves H2/H∞ cost performance. 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.
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