A GENERAL AND EXACT METHOD FOR DETERMINING LIMIT-CYCLES DECENTRALIZEDRELAY SYSTEMS

An exact method for evaluating the periods and stability of limit cycl es in decentralized relay systems is presented. The method can cope wi th relays having dead zones and hystereses. The underlying idea is to convert the continuous decentralized relay system under a limit cycle to an equivalent fictitious sampled-data system with synchronous sampl ers. Consequently, regular sampled-data tools can be applied in a stra ightforward manner to derive closed-form necessary conditions as well as stability conditions and other properties of such systems. This pap er extends and generalises recent results obtained by the authors.