H∞H∞ fuzzy control for nonlinear time-delay singular Markovian jump systems with partly unknown transition rates

This paper investigates the problem of H∞H∞ fuzzy control for a class of nonlinear time-delay singular Markovian jump systems with partly unknown transition rates. This class of systems under consideration is described by Takagi–Sugeno (T–S) fuzzy model. The goal of the paper is to design fuzzy state-feedback controllers such that systems with partly unknown transition rates are not only regular, impulse-free and stochastically stable, but also satisfy a prescribed H∞H∞ performance for all delays no larger than a given upper bound in terms of linear matrix inequalities. And systems with completely known transition rates can be viewed as a special case of the one we consider here. Finally numerical examples are given to illustrate the merit and usability of the approach proposed in this paper.