Approximately bisimilar symbolic model for switched systems with unstable subsystems

This paper deals with approximate bisimulation for the switched nonlinear system with mode-dependent dwell time. A criterion for incremental stability is presented for this switched nonlinear system by constructing incremental Lyapunov-like functions. Then for the case that all the subsystems are linear, a more solvable criterion is provided in terms of linear matrix inequalities. A symbolic model which is approximately bisimilar to the original switched nonlinear system is developed by using the grid-based approach, and the bisimilar precision is also given. Numerical examples are provided to show the application of the proposed results. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper addresses the approximate bisimulation problem for switched nonlinear systems with mode-dependent dwell time. It presents a criterion for incremental stability and a solvable criterion for the case of linear subsystems. Additionally, a symbolic model that is approximately bisimilar to the original system is developed using the grid-based approach, with the corresponding bisimilar precision provided.