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<p>In this work, we examine the approximate controllability results for second-order damped neutral stochastic differential systems that include state-dependent delay and impulses, which is crucial for understanding the dynamics of such systems. The analysis begins by establishing existence findings for the underlying system using cosine families of operators, multivalued analysis, stochastic processes, and applying the well-known fixed-point theorem for multivalued maps. This study explores the conditions under which controllability can be achieved, highlighting the impact of the impulsive effects and the state-dependent delay on the overall system behavior. Further, the controllability findings are obtained based on a set of suitable requirements. To demonstrate the theoretical conclusions relevance and efficacy, a thorough example is provided that shows how the created framework may be used to attain control performance in systems.</p>

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A Class of Second-Order Damped Neutral Stochastic Differential Control Systems with State-Dependent Delay and Impulses

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • R. Sasikumar,
  • V. Vijayakumar

摘要

In this work, we examine the approximate controllability results for second-order damped neutral stochastic differential systems that include state-dependent delay and impulses, which is crucial for understanding the dynamics of such systems. The analysis begins by establishing existence findings for the underlying system using cosine families of operators, multivalued analysis, stochastic processes, and applying the well-known fixed-point theorem for multivalued maps. This study explores the conditions under which controllability can be achieved, highlighting the impact of the impulsive effects and the state-dependent delay on the overall system behavior. Further, the controllability findings are obtained based on a set of suitable requirements. To demonstrate the theoretical conclusions relevance and efficacy, a thorough example is provided that shows how the created framework may be used to attain control performance in systems.