Decentralized H_∞ controller design: A matrix inequality approach using a homotopy method

This paper considers a decentralized H_∞ 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_∞ controller, to block-diagonal matrices of specified dimensions which describe a decentralized H_∞ controller. When a feasible decentralized H_∞ control problem is considered, it can be expected that there always exists a centralized H_∞ controller for which the algorithm converges and presents a desired solution. To find such a suitable centralized H_∞ controller, random search in a parametrized set of H_∞ controllers with a proper dimension is suggested. The efficiency of the proposed algorithm is demonstrated by an example.