Robust H∞ model reduction for a class of nonlinear time-varying systems with time delays

In this paper, we are concerned with the H_∞ model reduction problem for a class of nonlinear time-varying systems with parameter uncertainties and time delays in a discrete time framework. By introducing a proper Lyapunov function, we establish a sufficient condition ensuring the asymptotically mean square stability of the associate error system with a prescribed H_∞ error performance in the form of quasi-linear matrix inequality, based on which the parameters of the reduced-order model can also be determined. Finally, a numerical example is included to show the effectiveness of the developed technique.