Reachable Set Estimate Performance and Stochastic Aperiodic Sampling Mechanism Design for T-S Fuzzy Systems: Its Application to Wind Turbine System

The primary objective of this article is to develop the stochastic aperiodic sampled-data control (SASDC) mechanism for analyzing the reachable set estimate performance and stability properties of Takagi–Sugeno fuzzy systems against external disturbances. To do this, first, the sampling period is assumed to be time-varying, in which the addressed closed-loop system is modeled as a time-varying system based on an input-delay approach. Next, a reachable set lemma is proposed to deal with stochastic variables, and a novel free-weight matrix integral inequality is also introduced to reduce model conservatism. Further, assuming that the sampling period satisfies Bernoulli distribution and introduces stochastic variables to describe the unknown input delay and sampling period, a suitable discontinuous Lyapunov--Krasovskii functional is constructed, and some sufficient conditions are derived such that all states of the systems included by an ellipsoid region under zero initial condition. Also, an optimization control algorithm is proposed to understand the output feedback structure of the proposed SASDC scheme. Finally, to prove the effectiveness and applicability of the proposed theoretical observations, the numerical simulations of wind turbine systems are validated numerically by considering the experimental range of parameter values. Then, a comparative example is also given to emphasize the superiority and relevance of the proposed method. In addition to comparing with the existing studies, a maximal sampling-data period can be able to attain by this method.