Finite-time H∞ fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions.

This paper addresses a finite-time H∞ fuzzy control problem for a class of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions, which is represented as a Takagi–Sugeno (T–S) fuzzy model. A new homogeneous polynomial of partly uncertain transition rates is chosen. Free-matrix-based and double integral forms of the Wirtinger-based integral inequalities are employed to make the proposed approach less conservative. Then sufficient conditions are derived such that the fuzzy nonlinear Makovian jump delayed system exhibits stochastic finite-time boundedness. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methodology.