5/24/2016 Decentralized H∞ controller design: a matrix inequality approach using a homotopy method http://www.sciencedirect.com/science/article/pii/S0005109800001904 1/23 doi:10.1016/S00051098(00)001904 Automatica Volume 37, Issue 4, April 2001, Pages 565–572 Brief Paper Decentralized H ∞ controller design: a matrix inequality approach using a homotopy method ☆ Guisheng Zhai *, 1, a, , , Masao Ikeda *, 2, b , Yasumasa Fujisaki *, 3, c Show more Abstract 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. Keywords Decentralized control; H ∞ control; Dynamic output feedback; Matrix inequality; Homotopy method 1. Introduction This paper considers a decentralized H ∞ control problem for multichannel linear time invariant systems. At each control channel, the controller uses only locally measured output. For such systems, Wang and Davison (1973) introduced the notion of “fixed modes” and proved that a system is decentrally stabilizable if and only if it has no unstable fixed mode. Corfmat and Morse (1976) extended this result to a decentralized pole assignment problem and showed that nonexistence of any fixed mode is necessary and sufficient for arbitrary pole placement. As for H ∞ control, Date and Chow (1993) proposed a twostage optimal H ∞ decentralized controller design in which the first stage carries out an optimal centralized design and the second stage involves the optimization of introduced parameters that decentralize the optimal centralized controller. The idea is based on parametrization of concurrent decentralized observer controllers, which usually yields highdimensional local controllers. Paz (1993) proposed another decentralized H ∞ controller, in which each local controller is essentially a standard centralized H ∞ controller (Doyle, Glover, Khargonekar, Get rights and content