BMI Approach to Decentralized and Cooperative Control of Large-Scale System

Based on the bilinear matrix inequality (BMI) technique, the problems of designing decentralized controllers and cooperative controllers of linear large-scale systems are considered. Necessary and sufficient conditions of the optimal decentralized and cooperative stabilization of the linear large-scale systems are obtained. The problems of designing decentralized and cooperative controllers are formulated into the non-convex optimization problems with BMI constraints. To solve these problems, the alternate optimized algorithms are proposed. Finally, example is given to illustrate the main results. It shows that a large-scale system can be stabilized via cooperative controllers or decentralized controllers and needs not presumer each subsystem be stable.