On the absolute stability  of automatic control systems in the vicinity of a program manifold

Sailaubay  Zhumatov; Meiramgul Talipova; Zagira  Kobeyeva

doi:10.70474/d6kew891

Авторы

Сайлаубай Сагимбаевич Жуматов Институт математики и математического моделирования Автор https://orcid.org/0000-0001-7397-8999
Мейрамгуль Жубаткановна Талипова Актюбинский региональный университет имени К. Жубанова Автор https://orcid.org/0000-0001-9728-8378
Загира Сапарбековна Кобеева Шымкентский университет Автор

DOI:

https://doi.org/10.70474/d6kew891

Ключевые слова:

Программное многообразие, абсолютная устойчивость, нестационарная нелинейность, автоматические системы управления, функции Ляпунова, локальная квадратичная связь

Аннотация

Рассматривается задача построения систем автоматического управления по заданному программному многообразию. Сначала дается общий метод построения обыкновенных дифференциальных уравнений, который сводится к выбору некоторой функции, обеспечивающей устойчивость заданного многообразия. Затем абсолютная устойчивость систем автоматического управления исследуется в окрестности заданного многообразия. Нелинейности удовлетворяют условиям локальной квадратичной связи и они дифференцируемы по всем переменным. Достаточные условия абсолютной устойчивости программного многообразия, относительно заданной вектор-функции получены с помощью построения функции Ляпунова типа «квадратичная форма плюс интеграл от нелинейности». Установлены частотные условия абсолютной устойчивости программного многообразия систем управления. Также получены достаточные условия абсолютной устойчивости систем автоматического управления с нестационарными нелинейностями.

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