Decentralized H∞ 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 Feedback. The control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI). The objective of this paper is to propose an algorithm for solving the BMI by using the idea of the homotopy method, where the controller's coefficient matrices are deformed from full matrices defined by a centralized H(x) controller, to block-diagonal matrices of specified dimensions which describe a decentralized H(x) controller. When a feasible decentralized H(x) control problem is considered, it can be expected that there always exists a centralized H(x) controller for which the algorithm converges and presents a desired solution. To find such a suitable centralized H(x) controller, random search in a parametrized set of H(x) controllers with a proper dimension is suggested. The efficiency of the proposed algorithm is demonstrated by an example. (C) 2001 Published by Elsevier Science Ltd.