Special decentralized control problems and effectiveness of parameter-dependent Lyapunov function method

This paper is devoted to studying decentralized control problems from a special viewpoint and testing the effectiveness of parameter-dependent Lyapunov function method. First it is pointed out that in order to stabilize some given interconnected systems, some subsystems should be assigned to be unstable in some special cases. Then a special kind of decentralized control problem is studied. This kind of problem can be viewed as harmonic control among independent subsystems. Research results show that two unstable systems can generate a stable system through some effective cooperations. Linear matrix inequality (LMI)-based decentralized controller design method is also given for the special problems studied here by using parameter-dependent Lyapunov function method developed for robust stability.