Analysis and Verification of Input-to-State Stability for Nonautonomous Discrete-Time Switched Systems via Semidefinite Programming

This article concerns the theoretical analysis and mechanical verification of input-to-state stability (ISS) for nonautonomous discrete-time switched systems. To start with, based on a bounded function and the average dwell time, we successively propose less conservative sufficient conditions for uniform input-to-state stability, global uniform asymptotic input-to-state stability, and global uniform exponential input-to-state stability of nonautonomous switched nonlinear systems. Then, for systems with zero inputs, we apply our bounded function and average dwell time based method to further relax the sufficient conditions for their uniform stability, global uniform asymptotic stability, and global uniform exponential stability. Particularly, we propose a linear semidefinite programming based computable approach for mechanical verification of our current theoretical results for the rational (and even certain nonrational) nonautonomous switched systems. Note that our theoretical results and mechanical approach are both illustrated by examples.

Automated summary

This article presents a theoretical analysis and mechanical verification of input-to-state stability (ISS) for nonautonomous discrete-time switched systems. The authors propose less conservative sufficient conditions based on bounded functions and average dwell time for various types of stability, and introduce a linear semidefinite programming based computable approach for mechanical verification of theoretical results. Both the theoretical results and mechanical approach are illustrated through examples.