ДО ПИТАННЯ СТІЙКОСТІ ГІБРИДНИХ АВТОМАТІВ ЗА ЧАСТИНОЮ ЗМІННИХ
The problem of the stability of hybrid automata according to certain variables is considered. This problem is relevant and it is increasing rapidly, especially in recent years. Aspects of it's solution using the Lyapunov function are also considered. Theproblem of hybrid automata stability rega...
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| Date: | 2025 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2025
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| Subjects: | |
| Online Access: | https://jais.net.ua/index.php/files/article/view/677 |
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| Journal Title: | Problems of Control and Informatics |
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Problems of Control and Informatics| Summary: | The problem of the stability of hybrid automata according to certain variables is considered. This problem is relevant and it is increasing rapidly, especially in recent years. Aspects of it's solution using the Lyapunov function are also considered. Theproblem of hybrid automata stability regarding certain variables arises naturally while solving the applied problems. Namely, when, based on the requirements of the normal functioning of an object, it is sufficient to ensure its stability only according to some variables. Formulation of the problem of stability regarding certain variables belongs to A.M. Lyapunov, but he himself did not investigate this problem. There is a great methodological similarity in the study of stability considering all, and part ofvariables using Lyapunov functions. But there are certain differences in resolving some identical issues as applied to stability problems for all and part of the variables. There are methods to reduce the problem of stability regarding certain variables tothe study of stability in all variables of some auxiliary system, and vice versa. These two types of stability are closely related and mutually complementary. Currently, the problem of the stability of hybrid automata in terms of variables is considered as anindependent section of the theory of stability. It is shown that the property of y1 -positive definiteness of Lyapunov functions is not enough to investigate the stability of hybrid automata in terms of variables. The concept of a y1 -equable positive definitenessof a function had been introduced. Theorems that provide sufficient stability conditions had been proved. For linear hybrid automata, constructive stability conditions had been obtained. The article also shows how using the above theorems onecan investigate the stability of hybrid timed automata. |
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