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Delay-Dependent Functional Observer Design for Linear Systems With Unknown Time-Varying State Delays
Mohajerpoor, Reza,Shanmugam, Lakshmanan,Abdi, Hamid,Nahavandi, Saeid,Park, Ju H. IEEE 2018 IEEE transactions on cybernetics Vol.48 No.7
<P>Partial state estimation has numerous applications in practice. Nevertheless, designing delay-dependent functional observers (FOs) for systems with unknown time delays is rigorous and still an open dilemma. This paper addresses the problem for linear time-invariant systems with state time-varying delays. The delay is assumed to be bounded in an interval with a bounded derivative. A sliding mode FO structure that is robust against the delay uncertainties is established to this aim. The structure employs an auxiliary delay function that can be defined based on the existing knowledge on the actual delay values. Delay-dependent <I>sufficient</I> conditions for the stability of the observer are obtained using the Lyapunov Krasovskii approach, and are expressed in terms of a linear matrix inequality and two rank conditions. The <I>delay-free</I> observer structure is additionally studied and the <I>necessary and sufficient</I> conditions for its stability are obtained. Two descriptive numerical examples and simulation results demonstrate the design procedure and emphasize the effectiveness of the proposed observer design algorithm.</P>
Mani, Prakash,Rajan, Rakkiyappan,Shanmugam, Lakshmanan,Hoon Joo, Young Elsevier science 2019 Information sciences Vol.491 No.-
<P><B>Abstract</B></P> <P>The main concern of this paper is to address the synchronization problem of chaotic fractional-order fuzzy cellular neural networks (FOFCNNs) through designing the novel adaptive control scheme. The objective of the study is to explore the importance of considering fractional order derivatives (FODs) and time-varying delays. Even though numerous works have been reported in the literature regarding the derivation of sufficient conditions, there has been a lack of research on involving the dynamical analysis of FOFCNNs. Hence, this study focuses on the dynamical analysis of FOFCNNs. Particularly, both asymptotical and exponential synchronization of drive-response FOFCNN model is guaranteed via sufficient conditions that are derived by constructing the fractional Lyapunov functional candidate and solvable linear matrix inequalities (LMIs). Besides that, numerical simulations are performed to reveal the significance of the FODs. Also, an image encryption algorithm is designed based on the chaotic FOFCNNs solutions that result in better security measures. In summary, the overall contribution of the study is categorized into two: (1) sufficient conditions which ensure the global asymptotic and exponential stability are derived in a novel manner; (2) an image encryption algorithm is proposed by considering the FOFCNN as pseudo-random number generator (PRNG), which outperforms the existing encryption algorithms.</P>