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<p>For linear nonstationary singularly perturbed systems with small coefficients of some derivatives, the controllability problem in the class of impulse control is considered. We prove necessary and sufficient conditions of the differentiability of the impulse transition function that are independent of the small parameters. Based on the complete decomposition of the original system with respect to the action of a group of linear nondegenerate transformations, we obtain rank-type sufficient conditions for the impulse controllability of the system, which are independent of the small parameters and are valid for all sufficiently small values of them. The conditions are expressed in terms of the controllability matrices of the slow subsystem and the family of fast subsystems with dimensions smaller than the dimension of the original system.</p>

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CONTROLLABILITY OF LINEAR NONSTATIONARY SINGULARLY PERTURBED SYSTEMS IN THE CLASS OF IMPULSE CONTROLS

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • O. B. Tsekhan

摘要

For linear nonstationary singularly perturbed systems with small coefficients of some derivatives, the controllability problem in the class of impulse control is considered. We prove necessary and sufficient conditions of the differentiability of the impulse transition function that are independent of the small parameters. Based on the complete decomposition of the original system with respect to the action of a group of linear nondegenerate transformations, we obtain rank-type sufficient conditions for the impulse controllability of the system, which are independent of the small parameters and are valid for all sufficiently small values of them. The conditions are expressed in terms of the controllability matrices of the slow subsystem and the family of fast subsystems with dimensions smaller than the dimension of the original system.