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Functional observers design for nonlinear discrete-time systems with interval time-varying delays. (English) Zbl 1449.93071
Summary: This paper is concerned with the functional observer design for a class of multi-input multi-output discrete-time systems with mixed time-varying delays. Firstly, using the Lyapunov-Krasovskii functional approach, we design the parameters of the delay-dependent observer. We establish the sufficient conditions to guarantee the exponential stability of functional observer error system. In addition, for design purposes, delay-dependent sufficient conditions are proposed in terms of matrix inequalities to guarantee that the functional observer error system is exponentially stable. Secondly, we presented the sufficient conditions of the existence of internal-delay independent functional observer to ensure the estimated error system is asymptotically stable. Furthermore, some sufficient conditions are obtained to guarantee that the internal-delay independent functional observer error system is exponentially stable. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed method.
##### MSC:
 93B53 Observers 93C35 Multivariable systems, multidimensional control systems 93C55 Discrete-time control/observation systems 93C43 Delay control/observation systems 93C10 Nonlinear systems in control theory 93D23 Exponential stability
##### Software:
LMI toolbox; Matlab
Full Text:
##### References:
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