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Fuzzy sliding mode control design of Markovian jump systems with time-varying delay
Sakthivel, R.,Sakthivel, R.,Nithya, V.,Selvaraj, P.,Kwon, O.M. Elsevier 2018 Journal of the Franklin Institute Vol.355 No.14
<P><B>Abstract</B></P> <P>This paper studies the robust stochastic stabilization problem for a class of fuzzy Markovian jump systems with time-varying delay and external disturbances via sliding mode control scheme. Based on the equivalent-input-disturbance (EID) approach, an online disturbance estimator is implemented to reject the unknown disturbance effect on the considered system. Specifically, to obtain exact EID estimation Luenberger fuzzy state observer and a low-pass filter incorporated to the closed-loop system. Moreover, novel fuzzy EID-based sliding mode control law is constructed to ensure the stability of the closed-loop system with satisfactory disturbance rejection performance. By employing Lyapunov stability theory and some integral inequalities, a new set of delay-dependent robust stability conditions is derived in terms of linear matrix inequalities (LMIs). The resulting LMI is used to find the gains of the state-feedback controller and the state observer a for the resulting closed-loop system. At last, numerical simulations based on the single-link arm robot model are provided to illustrate the proposed design technique.</P>
Sakthivel, Rathinasamy,Sakthivel, Ramalingam,Kaviarasan, Boomipalagan,Wang, Chao,Ma, Yong-Ki Hindawi Limited 2018 Complexity Vol.2018 No.-
<P>The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.</P>
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>