Nonfragile $\mathcal{H}_{\infty}$ Control for Fuzzy Markovian Jump Systems Under Fast Sampling Singular Perturbation

This paper is concerned with the nonfragileH∞control problem for discrete-time fast sampling Markovian jump singularly perturbed nonlinear systems described by the Takagi-Sugeno fuzzy model. By utilizing singular perturbation theory, a singular perturbation parameter (SPP) independent, i.e., ε-independent, condition is derived to make sure the underlying closed-loop system's stability and a mixedH∞and passive performance γ, simultaneously. The ill-conditioned case caused by SPP could be eliminated on the basis of such a condition. With the aid of the stochastic analysis approach, the desired controller gains can be obtained, where the nonfragile property is fully considered to improve the tolerance of controller. Furthermore, a technique is developed to estimate the upper bound of SPP ε in this paper by employing a useful inequality. The availability and practicability of the proposed design method are finally explained via a practical example of a tunnel diode circuit with a modified model and a numerical example.