BMI Approach to the Interconnected Stability and Cooperative Control of Linear Systems

This paper studies the interconnected stability and cooperative control of large-scale linear systems. Using the technique of the bilinear matrix inequality (BMI), the necessary and sufficient conditions are given for interconnected stability and cooperative stabilization of two subsystems. It is shown that the systems can be cooperatively stabilized even if the subsystems are not stable. It is not necessary for us to presume the stability of the subsystems. Furthermore, the problems of designing interconnected and cooperative controllers are converted into the optimization problems using BMI constraints. To solve these problems, certain optimal alternate algorithms are proposed, and the proof for the convergence of the algorithms is presented. Finally, several examples are given to illustrate the optimization results.