The existence and uniqueness of the solutions of the nonlinear on-off switched systems with switching at variable times

In this paper, by introducing the definition of the solution, we prove the existence and uniqueness of the solution for nonlinear on-off switched systems with switching at variable times (NVTSS). Based on this result, the continuous dependence and differentiability of the solution of NVTSS (4) with respect to the initial state are presented. Besides, the switching phenomenon (the integral curve of NVTSS (4) may hit some surface finite or infinite times causing a rhythmical beating) and periodic solution of NVTSS (4) are also discussed.

Automated summary

This paper investigates the existence and uniqueness of solutions for nonlinear on-off switched systems with switching at variable times, as well as the continuous dependence and differentiability of the solutions with respect to the initial state. Additionally, the switching phenomenon and periodic solutions of the systems are also discussed.