On the general problem of solution and stability for variable-time switched systems

This paper copes with variable-time switched systems (UTSSs) whose integral curve is dependent on system state. According to classical theories, the conditions which guarantee the existence and the uniqueness of solution are proposed. The theoretical criteria for the absence and the possibility of beating phenomenon are also established. Under Razumikhin method and Lyapunov theorem, the exponential stability results for VTSS are also presented.