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Research Paper | Mathematics | Volume 15 Issue 6, June 2026 | Pages: 1385 - 1406 | India
Generalized Stabilization Theory for Switched Fuzzy Nonlinear Dynamical Systems via Multiple Lyapunov Functions and Linear Matrix Inequalities
Abstract: Switched fuzzy nonlinear dynamical systems have become an important research area owing to their ability to describe highly nonlinear processes with abrupt structural variations and uncertain operating conditions. Traditional stabilization techniques frequently rely on a common Lyapunov function, which may introduce unnecessary conservatism and reduce controller performance for complex switching mechanisms. This paper develops a generalized stabilization framework for continuous-time switched Takagi-Sugeno fuzzy nonlinear systems using multiple Lyapunov functions and linear matrix inequality (LMI) techniques. A novel family of mode-dependent Lyapunov functions is constructed to characterize subsystem stability under arbitrary and average dwell-time switching laws. Sufficient LMI-based stabilization conditions are established for state-feedback controller synthesis. Several new theoretical results including generalized stability criteria, switching-dependent decay conditions, robust stabilization theorems, and boundedness properties are derived with rigorous mathematical proofs. The proposed methodology signifcantly reduces conservatism while improving robustness against parameter uncertainty and switching disturbances. Numerical examples illustrate the e?ectiveness of the developed approach and demonstrate superior stabilization performance compared with conventional common Lyapunov function methods.
Keywords: Switched nonlinear systems, Takagi?Sugeno fuzzy systems, Multiple Lyapunov functions, Linear matrix inequalities, Robust stabilization
How to Cite?: Avinash Kumar, "Generalized Stabilization Theory for Switched Fuzzy Nonlinear Dynamical Systems via Multiple Lyapunov Functions and Linear Matrix Inequalities", Volume 15 Issue 6, June 2026, International Journal of Science and Research (IJSR), Pages: 1385-1406, https://www.ijsr.net/getabstract.php?paperid=SR26627160235, DOI: https://dx.doi.org/10.21275/SR26627160235