A new method for stabilization of a class of nonlinear discrete-time systems

In this paper, a new method for stabilization of a class of discrete time phase-controlled systems is proposed. Based on the geometrical interpretation of the frequency inequalities conditions of Lagrange stability of the system, the frequency conditions is equivalently converted into an H-infinity norm bound requirement, which makes it possible to solve the synthesis problems within the framework of H-infinity control theory. Linear dynamic output controller is constructed and the controller existence conditions are derived in terms of linear matrix inequalities (LMIs). With this LMI approach, the results are extended to the uncertain case with norm-bounded uncertainties in the linear part of the system. Illustrative example is given to show the feasibility of the proposed technique.