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Item CONTROLLABILITY OF IMPULSIVE DAMPED FRACTIONAL ORDER SYSTEMS INVOLVING STATE DEPENDENT DELAY (Article)(Universal Wiser Publisher, 2024) Arthi, G; Vaanmathi, MIn this article, the concept of controllability on fractional order impulsive systems involving state dependent delay and damping behavior is analysed by utilizing Caputo fractional derivative. The main motivation is to derive the sufficient conditions for the controllability of the considered systems. Based on the Laplace transform and inverse Laplace transform, the solution of fractional-order dynamical systems are obtained. The results are established by utilizing basic ideas of fractional calculus, Mittag-Leffler function and Banach fixed point theorem. Finally, an application is provided to illustrate the derived result.Item CONTROLLABILITY OF STOCHASTIC FRACTIONAL SYSTEMS INVOLVING STATE-DEPENDENT DELAY AND IMPULSIVE EFFECTS (Article)(Springer Science and Business Media Deutschland GmbH, 2024) Arthi, G; Vaanmathi, M; Ma, Yong-KiIn this paper, the controllability concept of a nonlinear fractional stochastic system involving state-dependent delay and impulsive effects is addressed by employing Caputo derivatives and Mittag-Leffler (ML) functions. Based on stochastic analysis theory, novel sufficient conditions are derived for the considered nonlinear system by utilizing Krasnoselkii’s fixed point theorem. Correspondingly, the applicability of the derived theoretical results is indicated by an exampleItem CONTROLLABILITY OF IMPULSIVE FRACTIONAL DAMPED INTEGRODIFFERENTIAL SYSTEMS WITH DISTRIBUTED DELAYS(Springer Science and Business Media Deutschland GmbH, 2024) Arthi, G; Sivasangari, RThis paper focuses on controllability results for impulsive fractional distributed delay systems with damping behavior, involving the Caputo fractional derivative (CFD) for both linear and integro-differential systems. For linear systems, controllability results are established through the controllability Grammian matrix and employing a control function. Sufficient conditions for the controllability of nonlinear systems are derived using the Schauder fixed point theorem. An example is provided to illustrate the theory.Item CONTROLLABILITY ANALYSIS OF IMPULSIVE MULTI-TERM FRACTIONAL-ORDER STOCHASTIC SYSTEMS INVOLVING STATE-DEPENDENT DELAY (Article)(Multidisciplinary Digital Publishing Institute (MDPI), 2023-10) Arthi, G; Vaanmathi, M; Ma, Yong-KiThis study deals with the controllability of multi-term fractional-order stochastic systems with impulsive effects and state-dependent delay that exhibit damping behavior. Based on fractional calculus theory, the Caputo fractional derivative is utilized to analyze the controllability of fractional-order systems. Mittag–Leffler functions and Laplace transform are used to derive the solution set of the problem. Sufficient conditions for the controllability of nonlinear systems are achieved using fixed-point techniques and stochastic theory. Finally, the results stated in the paper are validated using examples.Item ROBUST H∞ FILTER DESIGN FOR DISCRETE TIME SWITCHED INTERCONNECTED SYSTEMS WITH TIME-VARYING DELAYS(Elsevier Ltd, 2024-07-30) Arthi, G; Antonyronika, M; Yong-Ki, MaThe filter design of H∞ for an interconnecting system (IS) with uncertain discrete time switching is examined. Discrete-time N-linear subsystems with coupling states that have time delays, external disturbances and uncertainty are taken into account. Utilising Lyapunov-Krasovskii functional (LKF) and the Linear-Matrix-Inequality (LMI) approach, an appropriate filter is designed for the considered interconnected system. To remove an outside disruption, H∞ performances (HP) are implemented. Sufficient criteria are developed to assure the Exponentially Mean-Square Stability (EMSS). Then, using MATLAB-LMI toolbox filter parameters were established. Finally, the efficiency of the designed filter is illustrated with mathematical instances.Item CONTROLLABILITY OF STOCHASTIC FRACTIONAL SYSTEMS INVOLVING STATE-DEPENDENT DELAY AND IMPULSIVE EFFECTS(Springer Science and Business Media, 2024) Arthi, G; Vaanmathi, M; Yong-Ki, MaIn this paper, the controllability concept of a nonlinear fractional stochastic system involving state-dependent delay and impulsive effects is addressed by employing Caputo derivatives and Mittag-Leffler (ML) functions. Based on stochastic analysis theory, novel sufficient conditions are derived for the considered nonlinear system by utilizing Krasnoselkii’s fixed point theorem. Correspondingly, the applicability of the derived theoretical results is indicated by an exampleItem CONTROLLABILITY OF STOCHASTIC FRACTIONAL SYSTEMS INVOLVING STATE-DEPENDENT DELAY AND IMPULSIVE EFFECTS(Springer Open, 2024-01-30) Arthi, G; Vaanmathi, M; Yong-Ki, MaIn this paper, the controllability concept of a nonlinear fractional stochastic system involving state-dependent delay and impulsive effects is addressed by employing Caputo derivatives and Mittag-Leffler (ML) functions. Based on stochastic analysis theory, novel sufficient conditions are derived for the considered nonlinear system by utilizing Krasnoselkii’s fixed point theorem. Correspondingly, the applicability of the derived theoretical results is indicated by an example.Item EXISTENCE AND CONTROLLABILITY FOR IMPULSIVE FRACTIONAL STOCHASTIC EVOLUTION SYSTEMS WITH STATE-DEPENDENT DELAY(Journal of Applied Analysis and Computation, 2023) Arthi, G; Sivasangari, R; Yong-Ki, MaThis paper is concerned with the impulsive fractional stochastic neutral evolution systems with state-dependent delay and nonlocal condition. First, the existence of solutions of considered evolution systems are obtained by applying the Banach contraction theorem. Then, on the basis of existence of solutions, the controllability concept of the system is investigated. The main aim is to derive some conditions that could be applied to analyze the controllability results for the considered evolution systems involving state-dependent delay. Finally, the efficiency of theoretical analysis is verified by an example.Item APPROXIMATE CONTROLLABILITY OF NONLINEAR FRACTIONAL STOCHASTIC SYSTEMS INVOLVING IMPULSIVE EFFECTS AND STATE DEPENDENT DELAY(Universal Wiser Publisher, 2023-06-17) Arthi, G; Suriyapriya, NThis paper studies the analysis of approximate controllability for the fractional order neutral stochastic impulsive integro-differential systems involving nonlocal condition and State Dependent Delay (SDD). Sufficient conditions are designed to illustrate the evaluation of approximate controllability. It is exhibited that the proposed protocol can explicitly drive the results by Krasnoselskii's fixed point technique and semigroup theory. As a final point, the derived scheme is validated through an example.Item CONTROLLABILITY ANALYSIS OF IMPULSIVE MULTI-TERM FRACTIONAL-ORDER STOCHASTIC SYSTEMS INVOLVING STATE-DEPENDENT DELAY(MDPI, 2023-09-30) Arthi, G; Vaanmathi, M; Yong-Ki, MaThis study deals with the controllability of multi-term fractional-order stochastic systems with impulsive effects and state-dependent delay that exhibit damping behavior. Based on fractional calculus theory, the Caputo fractional derivative is utilized to analyze the controllability of fractional-order systems. Mittag–Leffler functions and Laplace transform are used to derive the solution set of the problem. Sufficient conditions for the controllability of nonlinear systems are achieved using fixed-point techniques and stochastic theory. Finally, the results stated in the paper are validated using examples.