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Rakkiyappan, R.,Maheswari, K.,Velmurugan, G.,Park, Ju H. Elsevier 2018 Neural networks Vol.105 No.-
<P><B>Abstract</B></P> <P>This paper investigates <SUB> H ∞ </SUB> state estimation problem for a class of semi-Markovian jumping discrete-time neural networks model with event-triggered scheme and quantization. First, a new event-triggered communication scheme is introduced to determine whether or not the current sampled sensor data should be broad-casted and transmitted to the quantizer, which can save the limited communication resource. Second, a novel communication framework is employed by the logarithmic quantizer that quantifies and reduces the data transmission rate in the network, which apparently improves the communication efficiency of networks. Third, a stabilization criterion is derived based on the sufficient condition which guarantees a prescribed <SUB> H ∞ </SUB> performance level in the estimation error system in terms of the linear matrix inequalities. Finally, numerical simulations are given to illustrate the correctness of the proposed scheme.</P>
Rakkiyappan, R.,Chandrasekar, A.,Park, J.H.,Kwon, O.M. Elsevier Ltd 2014 NONLINEAR ANALYSIS HYBRID SYSTEMS Vol.14 No.-
This paper deals with the problem of exponential synchronization of Markovian jumping neural networks with time-varying delays and variable sampling control. Several delay-dependent synchronization criteria are derived to ensure the convergence of the error systems, that is, the master systems stochastically synchronized with the slave systems. By employing an improved Lyapunov-Krasovskii functional (LKF) with the triple integral terms and combining the convex technique, two new sufficient conditions are derived to guarantee that a class of delayed neural networks (DNNs) to be globally exponentially stable. The information about the lower bound of the discrete time-varying delay is fully used in the LKF. Moreover, the conditions obtained in this paper are formulated in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. The maximum sampling intervals are obtained based on the design of mode-independent controller. Finally, three numerical examples are given to demonstrate the efficiency of the proposed theoretical results.
Rakkiyappan, R.,Sakthivel, N.,Park, J.H.,Kwon, O.M. Elsevier [etc.] 2013 Applied mathematics and computation Vol.221 No.-
In this paper, the problem of state estimation for Markovian jumping fuzzy cellular neural networks (FCNNs) using sampled-data with mode-dependent probabilistic time-varying delays is investigated. By developing a delay decomposition approach, the information of the delayed states can be taken into full consideration. By introducing a stochastic variable with a Bernoulli distribution, the information of probability distribution of the time-varying delay is considered and transformed into one with deterministic time-varying delay. The main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally asymptotically stable in the mean square. Based on the Lyapunov-Krasovskii functional including triple integral terms and decomposed integral intervals, delay-distribution-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.
Dharani, S.,Rakkiyappan, R.,Park, J.H. Elsevier BV 2017 Neurocomputing Vol. No.
<P>The intention of this paper is to explore the problem of pinning sampled-data synchronization of coupled reaction-diffusion neural networks with added inertia and time-varying delays. Through the proper variable substitution, the original system is transferred into first-order differential equations. Then, by constructing a suitable Lyapunov-ICrasovsidi functional (LKF), which uses more information of the delay bounds, global asymptotic synchronization criteria for the considered system are established in the form of LMIs. The acquired LMIs can be simply examined for their practicability by utilizing any of the accessible softwares. At last, two examples are furnished to manifest the efficacy of the derived criteria.</P>
Sivaranjani, K.,Rakkiyappan, R.,Joo, Young Hoon Elsevier 2018 Journal of the Franklin Institute Vol.355 No.8
<P><B>Abstract</B></P> <P>This paper focuses on the synchronization problem of semi-Markovian jumping complex dynamical networks with time-varying coupling delays against actuator failures. In an aim to shrink the treatment of network resources event triggered control strategy is proposed to achieve the synchronization criteria. By constructing Lyapunov–Krasovski functional, some delay dependent criteria that assures the synchronization of CDN are derived with the help of the general integral inequalities. It should be noted that the general integral inequality used here is general than that of Jensen inequality, the Wirtinger-based inequality, the Bessel-Legendre inequality, the Wirtinger-based double integral inequality, and the auxiliary function-based integral inequalities. The resulting LMIs can be easily verified with the help of the available softwares. Finally, simulation results are proposed to verify the effectiveness of the general integral inequality and designed control law.</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>
Mohajerpoor, R.,Shanmugam, L.,Abdi, H.,Rakkiyappan, R.,Nahavandi, S.,Park, J.H. Pergamon 2017 Journal of the Franklin Institute Vol. No.
<P>It is well-known that the stability analysis of time-delay systems is a key step to design appropriate controllers and/or filters for those systems. In this paper, the problem of the delay-dependent stability analysis of neutral systems with mixed interval time-varying delays with/without nonlinear perturbations is revisited. Bounded derivatives of the discrete and neutral delays with upper-bounds not limited to be strictly less than one are considered. New stability criteria are developed using the Lyapunov Krasovskii methodology which are expressed in terms of linear matrix inequalities (LMIs). An augmented Lyapunov Krasovskii functional (LKF) utilizing triple integral terms and the descriptor transformation is employed to this aim. In addition, advanced techniques such as Wirtinger-based single and double-integral inequalities, delay decomposition technique combined with the reciprocally convex approach, as well as a few effective free-weighting matrices are employed to achieve less conservative stability conditions. Comprehensive benchmarking numerical examples and simulation studies demonstrate the effectiveness of the proposed stability criteria with respect to some recently published results. The efficacy of the modern integral inequalities are also emphasized against the conventional.Tensen's inequalities. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.</P>
Lakshmanan, S.,Rihan, F.A.,Rakkiyappan, R.,Park, J.H. Elsevier Ltd 2014 NONLINEAR ANALYSIS HYBRID SYSTEMS Vol.14 No.-
In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov-Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.
Lakshmanan, S.,Park, Ju H.,Rihan, Fathalla A.,Rakkiyappan, R. Chinese Physical Society 2014 Chinese Physics B Vol.23 No.7
<P>We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov—Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.</P>