Observer design for a class of nonlinear systems subject to unknown inputs

We consider a novel method to design an observer for a class of nonlinear discrete-time systems with unknown inputs. Based on Lyapunov functional, we derive a sufficient condition for existence of the designed observer which requires solving a nonlinear matrix inequality. In light of linear algebra, the achieved condition will be formulated in terms of linear matrix inequality (LMI) that can be solved by popular methods easily. Compared to recent researches, the developed approach shows a significant better performance than other techniques previously published in literature and is less conservative in terms of Lipschitz constant. Finally, the proposed observer is illustrated by implementing the proposed method on a single-link flexible manipulator and the results are compared to some recent similar researches in terms of performance and conservativeness.