Stability of limit cycles with chattering in relay feedback systems

A relay feedback linear system with the transfer function of the pole excess equal to two can have a sliding mode in the set of co-dimension two and chattering mode around it. The chattering can be a part of a limit cycle in the relay feedback system and this limit cycle can be unique and globally stable. It was shown before that a limit cycle exists for a special class of systems with stable denominator and unstable numerator. In this paper, it is proved that the cycle is locally stable under the same conditions. An approach for global stability analysis was developed and illustrative results are shown.