Model reduction of a class of discrete-time nonlinear systems

This paper considers the problem of model reduction of a class of discrete-time systems subject to Lipschitzian nonlinearities. It is shown that under some conditions the nonlinear system can be either approximated by a discrete-time linear time-invariant system or a nonlinear system of reduced order. The computation of the matrices of the reduced-order system is carried out through the solutions of a set of linear matrix inequalities. The proposed design is approved by the simulation of reduced-order dynamics of a mass-spring system subject to a nonlinear friction and a linear electric circuit with uncertain parameters.