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Event‐triggered integral sliding mode control of Takagi‐Sugeno fuzzy stochastic systems

This article analyzes the integral sliding mode control (ISMC) problem for the nonlinear stochastic system by employing the fuzzy approach. Firstly, the Takagi‐Sugeno (T‐S) fuzzy stochastic model with unknown nonlinear function and external disturbance has been developed. Based on the fuzzy model, an observer‐based integral sliding mode fuzzy controller is derived under the event‐triggered scheme (ETS). The Lyapunov‐Krasovskii functionals (LKFs) involving double and triple integral terms are considered and evaluated by applying Writinger inequality lemma and reciprocally convex combination lemma. With the help of matrix's singular value decomposition lemma, the stability conditions have been derived which is in terms of linear matrix inequalities (LMIs) and this can be solved by MATLAB LMI toolbox. Two numerical examples are provided to demonstrate the usefulness of our theoretical conclusions.