Consistency and Lyapunov Stability of Linear Singular Time Delay Systems: a Geometric Approach

На практике при рассмотрении различных систем с управлением (химические инженерные системы, линии передачи без потерь, крупномасштабное управление электрической сетью, управление ориентацией самолета, гибкое управление руками роботов и т.д.) часто во многих ситуациях мы можем наблюдать наличие временного запаздывания. Вырожденные системы с запаздыванием являются динамическими системами, описываемыми взаимосвязанными алгебраическими и дифференциальными уравнениями. В данной работе исследуются геометрические представления начальных данных, которые обеспечивают гладкость решений рассматриваемых задач. Также изучается построение теории устойчивости Ляпунова для ограничения скорости убывания решений. Для одного класса изучаемых систем получены новые условия асимптотической устойчивости, зависящие от запаздывания. Более того, результат выражается в терминах матриц, которые задают систему и естественным образом возникают при моделировании, однако при этом отсутствует необходимость введения алгебраических преобразований в утверждение основной теоремы.

Ключевые слова

вырожденные системы с запаздыванием; устойчивость по Ляпунову; совместные начальные условия.

Литература

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