Stochastic H2/H∞ control of nonlinear systems with time-delay and state-dependent noise

This paper investigates the problem of H2/H∞ control for nonlinear stochastic systems with time-delay and state-dependent noise. Firstly, a sufficient condition for the existence of the nonlinear stochastic H2/H∞ control with time-delay is presented in terms of coupled Hamilton–Jacobi equations (HJEs). Secondly, by using the fuzzy approach, the stochastic H2/H∞ controller can be designed via solving a set of linear matrix inequalities instead of coupled HJEs. Finally, two numerical examples are employed to show the effectiveness of the results obtained.