Membership-Function-Dependent Design of Quantized Fuzzy Sampled-Data Controller for Semi-Markovian Jump Systems With Actuator Faults

This article concerns a fuzzy sampled-data controller for nonlinear semi-Markovian jump systems (SMJS) via the fuzzy dependent stochastic looped-Lyapunov functional (FSLF) approach. To do this, with the help of the Takagi–Sugeno (T–S) method, the stochastic jump parameters, actuator faults, and logarithmic quantizer are all considered in a unified framework. The stochastic parameters are generated by the semi-Markov process, whose transition rates depend upon the sojourn time. The nonlinear SMJS depicts real-time models subject to unpredictable structural changes, such as single-link robotic arm (S-LRA) systems. A key issue under consideration is how to design a fuzzy sampled-data controller to ensure stochastic stability for the nonlinear SMJS in the presence of actuator faults and state quantization. For this purpose, by using the weak infinitesimal operator of constructed FSLF, sufficient conditions are determined to realize the stochastic stability of the proposed nonlinear systems. Then, the stochastic stability conditions for the proposed sampled-data controller scheme can be derived under a linear matrix inequality framework. The validity of the theoretical findings is verified by Rossler’s chaotic systems. The S-LRA model is demonstrated to illustrate the applicability and efficacy of the proposed controller scheme.