Nonfragile <inline-formula> <tex-math notation="LaTeX">$\mathcal{H}_{\infty}$ </tex-math> </inline-formula> Control for Fuzzy Markovian Jump Systems Under Fast Sampling Singular Perturbation

Abstract

This paper is concerned with the nonfragile <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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 mixed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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.