Generic Stability Criteria for Switched Nonlinear Systems With Switching-Signal-Based Lyapunov Functions Using Takagi–Sugeno Fuzzy Model

IEEE Transactions on Fuzzy Systems(2022)

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Abstract
The aim of this article is to establish generic stability conditions for switched nonlinear systems with mode-dependent average dwell-time (MDADT) switching rules via Takagi–Sugeno (T–S) fuzzy modeling, which cover all unstable modes, all stable modes, and partially unstable modes as special cases. Different from traditional multiple and multiple discontinuous Lyapunov function (MDLF) methods, the proposed novel switching-signal-based multiple discontinuous Lyapunov function (SMDLF) approach divides each mode-running interval dynamically according to the actual switching of the system. The developed approach can not only yield less conservative bounds on the MDADT but can also handle all unstable subsystems, which cannot be done by means of the traditional MDLF. A class of SMDLF is constructed for continuous-time switched T–S fuzzy systems, and relaxed stability conditions are presented for the system with both stable and unstable subsystems, using a larger switching signal space. Then, novel stability conditions are deduced for all stable and unstable subsystems in terms of slow and fast MDADT switching signals, respectively. Finally, comparative simulation examples are provided to verify the advantages and effectiveness of the proposed approach.
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Key words
Mode-dependent average dwell time (MDADT),multiple discontinuous lyapunov function (MDLF),switched T–S fuzzy systems
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