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Ying Cui,Yurong Liu,Wenbing Zhang,Fuad E. Alsaadi 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.1
In this paper, stochastic stability is analyzed for a class of discrete-time switched neural networks, in which time-varying mixed delays and stochastic noise are considered. Specifically, benefitting from the triple summation term included in a new Lyapunov functional, time-varying distributed delays are tackled and a criterion of decay estimation for a non-switched neural network is firstly obtained. Subsequently, in view of average dwell time methodology and stochastic analysis, several sufficient conditions are obtained to ensure that the stochastic stability problem is solvable. Furthermore, the derived sufficient conditions reflect that the decay rate of the considered neural networks has a close relationship with average dwell time, upper and lower bounds of delays and intensity of stochastic noise. Finally, validity of the inferred conclusions is given by a simulated example.
Shuo Zhang,Wen-yue Cui,Fuad E. Alsaadi 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.9
This paper is concerned with the problem of adaptive neural tracking control for uncertain non-smooth nonlinear time-delay systems with a class of lower triangular form. Based on Filippov’s theory, the bounded stability and asymptotic stability are extended to the ones for the considered systems, which provides the theory foundation for the subsequent adaptive control design. In the light of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent system model, based on which, two types of controllers are designed by using adaptive neural network (NN) algorithm. The first designed controller can guarantee the system output to track a target signal with bounded error. In order to achieve asymptotic tracking performance, the other type of controller with proportional-integral(PI) compensator is then proposed. It is also noted that by exploring a novel Lyapunov-Krasovskii functional and designing proper controllers, the singularity problem frequently encountered in adaptive backstepping control methods developed for time-delay nonlinear systems with lower triangular form is avoided in our design approach. Finally, a numerical example is given to show the effectiveness of our proposed control schemes.
Yangling Wang,Jinde Cao,Haijun Wang,Fuad E. Alsaadi 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.5
This work focuses on the leader-following consensus problem for networks of dynamic agents, each of which has second-order nonlinear time-delayed dynamics. Event-triggered control and pinning control strategies are used in view of energy conservation. For each agent, the controller updates only when a properly presented event triggering condition is satisfied, which is based on the measurement errors and an exponential term. The network communication topology contains a directed spanning tree and only a fraction of follower agents can obtain the leader agent’s information. By virtue of the Lyapunov-Krasovskii functional method, the M−matrix theory and some algebraic inequalities, a sufficient condition for achieving leader-following consensus is established. The Zeno-behavior of triggered time sequence is excluded whether the consensus is reached or not. Finally, a simulation example is provided to demonstrate the proposed theoretical results.
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>
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.