On stability of switched nonlinear systems with time-scaling transformation

This paper considers a class of switched nonlinear systems with time-scaling transformation. A newconcept named ‘time-scaling transformational average dwell time’ is proposed, based on which two stability conditions for the original switched system are established that rely on each mode's dynamics of the transformational switched system and the characteristic of the time-scaling transformation. The new observation significantly extends existing stability results, especially for the case with unstable modes. A numerical example is given to illustrate the effectiveness of the proposed method.