Decentralized robust H∞ controller design: An LMI approach

The design of robust decentralized H_infin state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices is investigated. Based on the bounded real lemma the parameterization theorem for the existence of a robust decentralized H_infin state feedback controller is derived. This condition is expressed as the feasibility problem of a set of matrix inequalities. Based on that, three linear matrix inequality (LMI) methods are proposed to solve the problem: the direct LMI approach, iterative LMI approach and homotopy iterative LMI approach. The controller obtained has the block diagonal structure, enables the closed-loop large-scale system robust asymptotically stable and satisfies the given H_infin performance index. At last an example is given to demonstrate the effectiveness of the method presented in this paper