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Asymptotic stability of delayed stochastic genetic regulatory networks with impulses
Sakthivel, R,Raja, R,Marshal Anthoni, S Royal Swedish Academy of Sciences 2010 Physica scripta Vol.82 No.5
<P>In this paper, the asymptotic stability analysis problem is considered for a class of delayed stochastic genetic regulatory networks with impulses. Based on the Lyapunov stability technique and stochastic analysis theory, stability criteria are proposed in terms of linear matrix inequalities (LMI). It is shown that the addressed stochastic genetic regulatory networks are globally asymptotically stable if four LMIs are feasible, where the feasibility of LMIs can be readily checked by Matlab LMI toolbox. Finally, a numerical example is given to demonstrate the usefulness of the proposed result.</P>
Tracking Control Design for Markov Jump Systems With Time-varying Delay and External Disturbances
Muthusamy Vijayakumar,Selvaraj Marshal Anthoni,Rathinasamy Sakthivel,Dhafer Almakhles 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.7
This article intends to provide an effective output tracking control protocol and enhanced disturbance rejection performance for a class of continuous-time Markov jump systems (MJSs) with time-varying delay and external disturbances. Precisely, enhanced EID strategy combined with a proportional integral control is proposed to solve the output tracking problem for the addressed systems. In particular, an enhanced EID strategy can deal with the system flexibility and to increase disturbance rejection performance. The needed gain values for assuring the mean-square asymptotic stability of the MJSs are identified with the help of the Lyapunov-Krasovskii functional and linear matrix inequalities. The approach described in this paper can improve output tracking and disturbances rejection performance than some exiting results, which is explored through simulation results. Moreover, the legality of theoretical explorations is also verified by the RLC series circuit model.
Sakthivel, Rathinasamy,Santra, Srimanta,Marshal Anthoni, Selvaraj,Kuppili, Venkatanareshbabu THE INSTITUTION OF ENGINEERING AND TECHNOLOGY 2017 IET GENERATION TRANSMISSION AND DISTRIBUTION Vol.11 No.4
<P>This study addresses the design of sampled-data feedback L8 controller for synchronisation of chaotic systems with external disturbances. By employing a novel time-dependent Lyapunov function which is positive definite at sampling times but not necessary between the sampling times, a new set of sufficient conditions in terms of linear matrix inequality is derived to a design sampled-data L8 control for synchronisation. More precisely, the proposed synchronisation results depend on both the lower and upper bounds on sampling interval and also the available information of the actual sampling pattern is fully used. Further, based on the Lyapunov function, an asymptotic anti-synchronisation criterion is derived by analysing the corresponding anti-synchronisation error systems. Subsequently, a set of sampled-data synchronisation control is designed in terms of solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical example based on boost converter DC-DC model is employed to show the effectiveness of the proposed sampled-data L8 synchronisation and anti-synchronisation control scheme.</P>
Sakthivel, R.,Joby, Maya,Marshal Anthoni, S. Elsevier science 2017 Information sciences Vol.418 No.-
<P>This paper addresses the dissipativity based resilient sampled-data control problem for a class of stochastic systems with actuator failures. In particular, the controller is assumed to posses probabilistic actuator faults with different failure rates. Moreover, the controller gain fluctuation appears in a random way which obeys certain Bernoulli distributed white noise sequences. A new set of sufficient conditions is obtained in terms of linear matrix inequalities for the derivation of resilient dissipative sampled-data controller by constructing an appropriate Lyapunov-Krasovskii functional together with free-weighting matrix technique. Simulation studies are performed to verify the performance and effectiveness of the proposed control design technique. (C) 2017 Elsevier Inc. All rights reserved.</P>
Delay fractioning approach to robust exponential stability of fuzzy Cohen-Grossberg neural networks
Mathiyalagan, K.,Park, J.H.,Sakthivel, R.,Marshal Anthoni, S. Elsevier [etc.] 2014 Applied mathematics and computation Vol.230 No.-
In this paper, the problem of robust exponential stability analysis for a class of Takagi-Sugeno (TS) fuzzy Cohen-Grossberg neural networks with uncertainties and time-varying delays is investigated. A generalized activation function is used, and the assumptions such as boundedness, monotony and differentiability of the activation functions are removed. By using a Lyapunov-Krasovskii functional and employing the delay fractioning approach, a set of sufficient conditions are established for achieving the required result. The obtained conditions are proposed in terms of linear matrix inequalities (LMIs), so its feasibility can be checked easily via standard numerical toolboxs. The main advantage of the proposed criteria lies in its reduced conservatism which is mainly based on the time delay fractioning technique. In addition to that, a numerical example with simulation results is given to show the effectiveness of the obtained LMI conditions.
Dissipative Based Adaptive Reliable Sampled-data Control of Time-varying Delay Systems
Santra, Srimanta,Karimi, Hamid Reza,Sakthivel, Rathinasamy,Anthoni, S. Marshal Institute of Control, Robotics and Systems 2016 International Journal of Control, Automation, and Vol.14 No.1
This paper is concerned with the problem of dissipative based adaptive reliable controller for a class of time delay systems subject to actuator failures and time-varying sampling with a known upper bound on the sampling intervals. By constructing a proper Lyapunov-Krasovskii functional which fully uses the available information about the actual sampling pattern and time delays, a new set of sufficient conditions is derived to obtain the required result. Then, a dissipative based adaptive sampled-data controller is designed such that the resulting closed-loop system is reliable in the sense that it is asymptotically stable and has the prescribed dissipative performance under given constraints. The existence condition of the desired dissipative based adaptive reliable sampled-data controller is obtained in terms of linear matrix inequalities. Further, the performance of the proposed controller is implemented on a liquid propellant rocket motor with a pressure feeding system model. The simulation results show the effectiveness and better performance of the proposed adaptive reliable sampled-data controller over conventional reliable controller.
CONTROLLABILITY OF SECOND ORDER SEMILINEAR VOLTERRA INTEGRODIFFERENTIAL SYSTEMS IN BANACH SPACES
Balachandran, K.,Park, J.Y.,Anthoni, S.-Marshal Korean Mathematical Society 1999 대한수학회보 Vol.36 No.1
Sufficient conditions for controllability of semilinear second order Volterra integrodifferential systems in Banach spaces are established using the theory of strongly continuous cosine families. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.
Dissipativity based repetitive control for switched stochastic dynamical systems
Sakthivel, R.,Saravanakumar, T.,Kaviarasan, B.,Marshal Anthoni, S. Elsevier [etc.] 2016 Applied mathematics and computation Vol.291 No.-
<P>This paper addresses the issues of dissipativity analysis and repetitive control synthesis for a class of switched stochastic dynamical systems with time-varying delay. By using the lifting technique, the considered one dimensional model is converted into a continuous-discrete stochastic two dimensional delayed model to describe the control and learning actions of the repetitive controller. By employing stochastic system theory together with Lyapunov function technique, a new set of sufficient conditions in terms of linear matrix inequalities (LMIs) is established such that the switched stochastic system in two dimensional delayed model is mean square asymptotically stable and (Q, S, R)-dissipative. Then, the desired repetitive controller is designed by solving a convex optimization problem established in terms of LMIs. More precisely, repetitive controllers with H-infinity, passivity and mixed H-infinity and passivity performances can be obtained as the special cases for the considered system. Finally, numerical examples are provided to demonstrate the effectiveness and potential of the developed design technique. (C) 2016 Elsevier Inc. All rights reserved.</P>