Reliable Control of Fuzzy Singularly Perturbed Systems and Its Application to Electronic Circuits

In this paper, the reliable control problem of nonlinear singularly perturbed systems subject to random actuator faults is studied. A Takagi-Sugeno fuzzy model is utilized to describe the nonlinear plant, and a Markov chain with partly unknown transition probabilities is adopted to characterize the random behaviors of the actuator faults, in contrast with the existing fault modes in which all the transition probabilities are required to be known. Combining the utilization of a novel fuzzy singular-perturbation-parameter-dependent Markovian Lyapunov function with the introduction of the slack matrix variable, sufficient conditions on the existence of the reliable fuzzy controller are presented, which are dependent on the upper bounds on the time derivatives of membership functions. A search algorithm is provided to obtain the maximum stabilization bound. Moreover, conditions based on single Lyapunov function are also established. The effectiveness and the applicability of the proposed new design technique are verified by an example of an electronic circuit system.