# Article

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Keywords:
functional observer; discrete-time systems; exponential stability; interval time-varying delays; Lyapunov–Krasovskii functional
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.
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