Local stability of limit cycles for time-delay relay-feedback systems

This brief is concerned with the local stability of limit cycles for linear systems under relay feedback, for the cases where the linear system includes a time-delay in its dynamics and the relay can possess asymmetric hysteresis. The limit cycle considered can be asymmetric, have more than two switchings a period, zero output derivatives at the switching instants. It shows that if a certain constructed matrix is Schur stable, then, the local stability of the considered limit cycle is guaranteed. The effectiveness of the presented results is illustrated by a numerical example.