A new method of reachable sets estimation for the nonlinear switched singular system with impulsive performance and time-delay

This paper addresses the reachable set problem on nonlinear switched singular systems with impulsive performance and time-delay under bounded disturbance. The goal is to provide a real-time bounding set containing all reachable states. Originally, a real-time bounding criterion is developed by analyzing the variation of subinterval piecewise function and combining the definition of the average impulsive interval. Additionally, a lower bound on the Lyapunov function is provided by introducing an inequality scaling technique to avoid acquiring state bounds based on system decomposition techniques. Subsequently, the real-time bounding closed set, including all reachable states of the system, is estimated by calculating the Dini derivative of the Lyapunov function and using the real-time bounding criterion and the integral inequality technique. Finally, several numerical examples are given to illustrate the validity of the results obtained in this study.