Robust decentralized mixed H2/H∞ dynamic output control for interconnected systems

This paper considers a decentralized mixed H
₂
/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 H
₂
/H
_∞
controller to exist, which achieves H
₂
/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.