LMIによる分散安定化制御装置の一設計法

A number of design methods for output-feedback decentralized stabilizing controllers have been proposed for large-scale linear systems. In the centralized case, it is well known that this output-feedback synthesis problem is reduced to an optimization problem of linear matrix inequalities (LMI’s). In this paper, to design decentralized controllers, we restrict some variables of those LMI’s to block-diagonal forms. However, since this restriction is not enough to obtain decentralized controllers, we also introduce a certain replacement of variables. Since the latter causes the LMI’s to turn into bilinear matrix inequalities (BMI’s), we convert BMI’s into LMI’s by fixing some variables in the BMI’s. We get two kinds of LMI’s which are obtained by fixing some variables and solve those LMI’s alternately. The effectiveness of this design method is illustrated by numerical examples.