Decentralized H-infinity controller design: a matrix inequality approach using a homotopy method

This paper considers a decentralized H-x control problem for multi-channel linear time-invariant systems. Our interest is focused on dynamic output Fe edback. The control problem is reduced to a feasibility problem of a biline ar matrix inequality (BMI). The objective of this paper is to propose an al gorithm for solving the BMI by using the idea of the homotopy method, where the controller's coefficient matrices are deformed from full matrices defi ned by a centralized H-x controller, to block-diagonal matrices of specifie d dimensions which describe a decentralized H-x controller. When a feasible decentralized H-x control problem is considered, it can be expected that t here always exists a centralized H-x controller for which the algorithm con verges and presents a desired solution. To find such a suitable centralized H-x controller, random search in a parametrized set of H-x controllers wit h a proper dimension is suggested. The efficiency of the proposed algorithm is demonstrated by an example. (C) 2001 Published by Elsevier Science Ltd.