Robust H∞ control of a class of nonlinear systems with delayed state and control: a LMI approach

Considers the problem of robust H_∞ control of a class of nonlinear systems with delayed state and control. The uncertainties we allow include both norm bounded and nonlinear uncertainties. The nonlinear uncertainties are assumed to satisfy a matching condition and bounded by a known continuous nonlinear function. Based on a linear matrix inequality (LMI) approach, we develop a state feedback controller design procedure which guarantees, the so-called L ₂-gain from the exogenous input noise to the state is minimized or no larger than a prescribed value. Finally we show that in some case if the delay of system is large, our result is less conservative than the delay-dependent results