Global Stability of Limit Cycles for a Class of MIMO Relay Feedback Systems

The global stability problem of limit cycles for decentralized relay feedback systems is studied.The key idea is to reduce the global stability problem to the asymptotic stability of an uncertain discrete-time system.As a result,a sufficient condition is obtained for the stability test.It shows that under some constraints all system trajectories will eventually enter and remain in a specific region,and tend to the considered limit cycle.A numerical example is given to illustarte the use of the present result.