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Samidurai, R.,Manivannan, R.,Ahn, Choon Ki,Karimi, Hamid Reza IEEE 2018 IEEE transactions on systems, man, and cybernetics Vol.48 No.4
<P>This paper examines the problem of asymptotic stability criteria for Markovian jump generalized neural networks with successive time-varying delay components. Generalized neural networks consist of a finite number of modes, which may jump from one mode to another according to a Markovian chain with known transition probability. By constructing novel augmented Lyapunov–Krasovskii functionals (LKFs) with triple integral terms that contain more and more information on the state vectors of the NNs, the upper bound of the successive time-varying delays is formulated. By employing a new integral inequality technique, free-weighting matrix-based integral inequality approach, and Wirtinger double integral inequality technique and that is combined with the reciprocally convex combination approach to estimate the single and double integral terms in the time derivative of the LKFs, a new set of delay-dependent conditions for the asymptotic stability of the considered NNs are represented in the form of linear matrix inequalities. Finally, five numerical examples are given to verify the effectiveness of the proposed approach with a four-tank benchmark real-world problem.</P>
R. Samidurai,S. Rajavel,R. Sriraman,Ahmed Alsaedi,Fuad E. Alsaadi,Jinde Cao 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.4
The objective of this paper is to analyze the stability analysis of neutral-type neural networks with additivetime-varying delay and leakage delay. By constructing a suitable augmented Lyapunov-Krasovskii functionalwith triple and four integral terms, some new stability criteria are established in terms of linear matrix inequalities,which is easily solved by various convex optimization techniques. More information of the lower and upper delaybounds of time-varying delays are used to derive the stability criteria, which can lead less conservative results. Theobtained conditions are expressed with linear matrix inequalities (LMIs) whose feasible can be checked easily byMATLAB LMI control toolbox. Finally, two numerical examples are given to demonstrate the effectiveness of theproposed method.
Manivannan, R.,Samidurai, R.,Cao, Jinde,Alsaedi, Ahmed,Alsaadi, Fuad E. Elsevier 2018 Chaos, solitons, and fractals Vol.114 No.-
<P><B>Abstract</B></P> <P>This paper addresses an improved stability criterion for an interval time-delayed neural networks (NNs) including neutral delay and leakage delay. By proposing a suitable Lyapunov–Krasovskii functionals (LKFs) together with the Auxiliary function-based integral inequality (AFBII) and reciprocally convex approach (RCC) approach. The major purpose of this research is put forward to the consideration of inequality techniques together with a suitable LKFs, and mixed with the Leibniz–Newton formula within the structure of linear matrix inequalities (LMIs). It is amazing that, the leakage delay has a disrupting impact on the stability behaviour of such system and they cannot be neglected. Finally, numerical examples have been demonstrated to showing feasibility and applicability of the developed technique. In addition, the developed stability criteria tested for feasibility of the benchmark problem to explore the real-world application in the sense of discrete time-delay and leakage delay as a process variable in the system model.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Some new mathematical technique is adapted together with L-K functionals are estimated its derivative via delay-partitioning approach, which has not been considered yet in stability of model (1) with interval time-varying delays and leakage delays are introduced. </LI> <LI> Different from others in [12,15,16,18,21,22,27,33,44,47], several numerical examples are presented to illustrate the validity of the main results with a real-world simulation. This implies that the results of the present paper are essentially new. </LI> <LI> Additionally, Wirtinger double integral inequality (WDII) technique is taken into account to bound the time-derivative of triple integral Lyapunov–Krasovskii functionals (LKFs), which provide more tighter bounding technology to dealing with such LKFs, this technique has been never used in previous literature ****[12,15,16,18,21,22,27,33,44,47], which play an important role in reducing conservatism. ***** </LI> </UL> </P>
New exponential stability criteria for stochastic BAM neural networks with impulses
Sakthivel, R,Samidurai, R,Anthoni, S M Royal Swedish Academy of Sciences 2010 Physica scripta Vol.82 No.4
<P>In this paper, we study the global exponential stability of time-delayed stochastic bidirectional associative memory neural networks with impulses and Markovian jumping parameters. A generalized activation function is considered, and traditional assumptions on the boundedness, monotony and differentiability of activation functions are removed. We obtain a new set of sufficient conditions in terms of linear matrix inequalities, which ensures the global exponential stability of the unique equilibrium point for stochastic BAM neural networks with impulses. The Lyapunov function method with the Itô differential rule is employed for achieving the required result. Moreover, a numerical example is provided to show that the proposed result improves the allowable upper bound of delays over some existing results in the literature.</P>
Quanxin Zhu,R. Raja,S. Senthilraj,R. Samidurai 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.5
This paper focuses on the stability analysis for neutral systems with discrete and distributed constanttime-delays. Lyapunov-Krasovskii functionals (LKFs) are constructed by non uniformly dividing the whole delayinterval into multiple segments and choosing proper functionals with different weighting matrices coressponding todifferent segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteriaare established for the neutral system in the delay partition approach. By utilizing the delay partition approach, theobtained stability criteria are stated in terms of linear matrix inequalities. Finally, some numerical examples areprovided to illustrate the effectiveness of the proposed approach less conservative than the existing ones.