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Observer design for a class of nonlinear discrete-time systems with time-delay. (English) Zbl 1264.93144
Summary: The problem of observer design for a class of nonlinear discrete-time systems with time-delay is considered. A new approach of nonlinear observer design is proposed for this class of systems. Based on differential mean value theory, the error dynamic is transformed into linear parameter variable system. By using Lyapunov’s stability theory and Schur’s complement lemma, sufficient conditions expressed in terms of matrix inequalities are obtained to guarantee the observer error converges asymptotically to zero. Furthermore, the problem of observer design with affine gain is investigated. The computing method for observer gain matrix is given and it is also demonstrated that the observer error converges asymptotically to zero. Finally, an illustrative example is given to validate the effectiveness of the proposed method.

##### MSC:
 93C55 Discrete-time control/observation systems 93B07 Observability 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D20 Asymptotic stability in control theory 93C83 Control/observation systems involving computers (process control, etc.) 93B40 Computational methods in systems theory (MSC2010)
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