LMI-based reduced-order observers for some discrete nonlinear systems

Stabilization of a nonlinear system by the use of state estimate feedback when the state variables are not available for measurement, has been an important research topic in control theory. In the paper, a reduced-order observer design is presented for a class of discrete time nonlinear systems. This is motivated by its potential use in dynamic feedback control of this class of discrete-time nonlinear systems in the presence of disturbances. These disturbances are assumed to be of finite energy type in this paper. The system model is a generalization of the discrete counterpart of the one in Thau (1974). We consider the LMI-based design of reduced-order observers for this model which will guarantee boundedness of a quadratic function of the estimation error or the boundedness of its energy