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Robust stability analysis of Takagi-Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays

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Chinese Physics B 2011年第8期20卷 1-15页

作者： m.syed ali Department of mathematics Thiruvalluvar UniversityVellore-632 106TamilnaduIndia

In this paper, the global stability of Takagi-Sugeno （TS） uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays （TSUSFRNNs） is considered. A novel LmI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs. The proposed stability conditions are demonstrated through numerical examples. Furthermore, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed. Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.

关键词： recurrent neural networks linear matrix inequality Lyapunov stability time-varyingdelays TS fuzzy model

Stability analysis of markovian jumping stochastic Cohen Grossberg neural networks with discrete and distributed time varying delays

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Chinese Physics B 2014年第6期23卷 131-137页

作者： m.syed ali Department of mathematics Thiruvalluvar University

In this paper, the global asymptotic stability problem of markovian jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays （mJSCGNNs） is considered. A novel LmI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of mJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen-Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.

关键词： Cohen-Grossberg neural networks global asymptotic stability linear matrix inequality Lyapunovfunctional time-varying delays

Robust H_∞ control for uncertain markovian jump systems with mixed delays

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Chinese Physics B 2016年第7期25卷 108-113页

作者： R Saravanakumar m syed ali Department of mathematics Thiruvalluvar University

We scrutinize the problem of robust H∞control for a class of markovian jump uncertain systems with interval timevarying and distributed delays. The markovian jumping parameters are modeled as a continuous-time finite-state markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional（LKF）, sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities（LmIs）. The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.

关键词： linear matrix inequality Lyapunov method markovian jumping parameters robust H∞ control

STOCHASTIC STABILITY OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH mARKOVIAN JUmPING PARAmETERS

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Acta mathematica Scientia 2015年第5期35卷 1122-1136页

作者： m.syed ali Department of mathematics Thiruval luvar University

In this paper, global robust stability of uncertain stochastic recurrent neural networks with markovian jumping parameters is considered. A novel Linear matrix inequal- ity（LmI） based stability criterion is obtained to guarantee the asymptotic stability of uncertain stochastic recurrent neural networks with markovian jumping parameters. The results are derived by using the Lyapunov functional technique, Lipchitz condition and S-procuture. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in [31] and [34] to show the effectiveness and conservativeness.

关键词： Lyapunov functional linear matrix inequality markovian jumping parameters recurrent neural networks

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

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Chinese Physics B 2014年第12期23卷 5-13页

作者： m.syed ali R.Saravanakumar Department of mathematics Thiruvalluvar University

In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LmIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.

关键词： distributed delay interval time-varying delay H∞control linear matrix inequality(LmI) stochastic systems

Robust H_∞ control of uncertain systems with two additive time-varying delays

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Chinese Physics B 2015年第9期24卷 25-34页

作者： m.syed ali R.Saravanakumar Department of mathematics Thiruvalluvar University

This paper is concerned with the problem of delay-dependent robust H∞control for a class of uncertain systems with two additive time-varying delays. A new suitable Lyapunov–Krasovskii functional（LKF） with triple integral terms is constructed and a tighter upper bound of the derivative of the LKF is derived. By applying a convex optimization technique, new delay-dependent robust H∞stability criteria are derived in terms of linear matrix inequalities（LmI）. Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically ***, numerical examples are given to illustrate the effectiveness of the proposed method. Comparison results show that our results are less conservative than the existing methods.

关键词： additive time-varying delays Lyapunov method H∞ control linear matrix inequality

Augmented Lyapunov approach to H_∞ state estimation of static neural networks with discrete and distributed time-varying delays

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Chinese Physics B 2015年第5期24卷 140-147页

作者： m.syed ali R.Saravanakumar Department of mathematics Thiruvalluvar University

This paper deals with H∞ state estimation problem of neural networks with discrete and distributed time-varying delays. A novel delay-dependent concept of H∞ state estimation is proposed to estimate the H∞ performance and global asymptotic stability of the concerned neural networks. By constructing the Lyapunov-Krasovskii functional and using the linear matrix inequality technique, sufficient conditions for delay-dependent H∞ performances are obtained, which can be easily solved by some standard numerical algorithms. Finally, numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results.

关键词： distributed delay H∞ state estimation neural networks stability analysis

SAmPLED-DATA STATE ESTImATION FOR NEURAL NETWORKS WITH ADDITIVE TImE–VARYING DELAYS

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Acta mathematica Scientia 2019年第1期39卷 195-213页

作者： m.syed ali N.GUNASEKARAN Jinde CAO Department of mathematics Thiruvalluvar University Research Center for Wind Energy Systems Kunsan National University School of mathematics Southeast University

In this paper, we consider the problem of delay-dependent stability for state estimation of neural networks with two additive time–varying delay components via sampleddata control. By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms and by using Jensen's inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities(LmIs) to ensure the asymptotic stability of the equilibrium point of the considered neural networks. Instead of the continuous measurement,the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. Due to the delay-dependent method, a significant source of conservativeness that could be further reduced lies in the calculation of the time-derivative of the Lyapunov functional. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components. Finally, numerical example is given to show the superiority of proposed method.

关键词： Lyapunov method linear matrix inequality state estimation sample-data control time-varying delays

SYNCHRONIZATION OF mASTER-SLAVE mARKOVIAN SWITCHING COmPLEX DYNAmICAL NETWORKS WITH TImE-VARYING DELAYS IN NONLINEAR FUNCTION VIA SLIDING mODE CONTROL

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Acta mathematica Scientia 2017年第2期37卷 368-384页

作者： m.syed ali J.YOGAmBIGAI 曹进德 Department of mathematics Thiruvalluvar UniversityVellore 632115Tamil NaduIndia Department of mathematics Southeast UniversityNanjing 210096China Department of mathematics Faculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia

In this article, a synchronization problem for master-slave markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LmIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

关键词： markovian switching complex dynamical networks Lyapunov-Krasovskii method sliding mode control Linear matrix Inequality