An Exponential Stabilization Analysis for Switched Interval Type-2 Fuzzy Sampled-Data Control Systems

Abstract

This work is focused on designing the admissible edge-dependent average dwell time (AE-DADT) based fuzzy sampled-data control problem for a class of switched nonlinear systems. The upper and lower grade of membership functions is used to characterize uncertain parameter-dependent nonlinear systems in the interval type-2 fuzzy (IT2F) model. Unlike from the existing literature, a new fuzzy dependent refined looped-Lyapunov functional (LF) is introduced which involves the new exponent terms and state information such as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\frac{e^{2\gamma _{v}(\varrho -\varrho _{\mathscr {k}})}-1}{2\gamma _{v}}, \ \frac{e^{2\gamma _{v}(\varrho _{\mathscr {k}+1}-\varrho)}-1}{2\gamma _{v}}, \ \mathscr {z}(\varrho _{\mathscr {k}})$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {z}(\varrho _{\mathscr {k}+1})$</tex-math></inline-formula> with tuning parameters and few slack variables. The AE-DADT switching property has also been taken into account for nonlinear systems, and it contributes to getting more information about previous modes. Based on the proposed new refined looped-LFs, new sufficient conditions are derived in terms of linear matrix inequalities (LMI), which ensure the global uniform exponential stability (GUES) of the nominated switched IT2F systems. The feasibility of the obtained results is verified by the numerical example, and the tunnel diode circuit system model and Lorenz chaotic system are established to illustrate the feasibility and efficacy of the theoretical findings.