A class of nonlinear observers for discrete-time systems with parametric uncertainty

In this paper the problem of observer design is considered for a class of nonlinear discrete-time systems with parametric uncertainty. The problem addressed aims at designing the gain-scheduled state observers such that, for all admissible nonlinearities and time-varying parameter uncertainties in the state equation, the observation process is asymptotically stable. An effective, purely algebraic methodology is developed to solve the proposed problem for discrete-time systems. It is shown that the solution is related to a generalized Riccati-like matrix equation. Specifically, by using the generalized inverse theory and singular value decomposition technique, we obtain the conditions for the existence of desired robust nonlinear observers and then characterize the explicit expression of these observers. Two numerical examples are used to demonstrate the applicability and flexibility of the present approach.