Stability Analysis of Switched Nonlinear Systems With Multiple Time-Varying Delays

• Published in: IEEE transactions on systems, man, and cybernetics. Systems man, and cybernetics. Systems, 2022-06, Vol.52 (6), p.3947-3956
• Main Authors: Wang, Zhichuang, Sun, Jian, Chen, Jie
• Format: Article
• Language: English
• Subjects: Delay effects; Delays; Functionals; Fuzzy systems; Liapunov functions; Mathematical analysis; Mathematical models; Multiple time-varying delays (MTVDs); Nonlinear systems; Numerical stability; Power system stability; stability; Stability analysis; Stability criteria; Subsystems; switched nonlinear systems (SNSs); Switches; unstable modes; Upper bounds
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2021.3080278

This article addresses the stability problem of switched nonlinear systems (SNSs) with multiple time-varying delays (MTVDs) whose subsystems are all unstable. By utilizing a multiple Lyapunov-Krasovskii functionals technique, some stability criteria for SNSs with MTVDs are obtained. To tackle the challenge of finding appropriate Lyapunov functions, we introduce Takagi and Sugeno (T-S) fuzzy models and present stability criteria for switched T-S fuzzy systems with MTVDs. Moreover, a novel switching signal is developed to eliminate the effect of the increment energy of Lyapunov functions for all unstable modes. The upshots of our result are that: 1) it allows the upper bound of the derivatives of Lyapunov functionals to be mode-dependent functions which can be positive or negative and 2) it also improves upon the existing results by removing several restrictive conditions. Finally, the effectiveness of our method is validated through numerical simulations.