66466

Автор(ы): 

Автор(ов): 

2

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Robust Stability Conditions for a Family of Linear Discrete-Time Systems Subject to Uncertainties

ISBN/ISSN: 

0005-1179

DOI: 

10.1134/S0005117921080117

Наименование источника: 

  • Automation and Remote Control

Обозначение и номер тома: 

Vol. 82, No.8.

Город: 

  • New York

Издательство: 

  • Pleiades Publishing, Ltd

Год издания: 

2021

Страницы: 

1456-1462
Аннотация
Robust stability conditions are established for a family of linear discrete-time systems subjected to uncertainties. The traditional approach, which involves the construction of a common quadratic Lyapunov function for the entire family of systems with uncertainty, often leads to the problem of conservatism. In this connection, constructing parametric quadratic Lyapunov functions seems promising. The main tools of the proposed approach are the apparatus of linear matrix inequalities and a modification, presented here, of the well-known Petersen’s lemma. A simple approach to finding the robust quadratic stability radius of the family in question is proposed in the paper as well. The corresponding optimization problems have the form of semidefinite programming and one-dimensional minimization, which can be easily solved numerically. The efficiency of our approach is demonstrated via a numerical example. The results obtained can be generalized to design problems for linear discrete-time systems subjected to uncertainties, to other robust statements, and to the case of exogenous disturbances.

Библиографическая ссылка: 

Хлебников М.В., Квинто Я.И. Robust Stability Conditions for a Family of Linear Discrete-Time Systems Subject to Uncertainties // Automation and Remote Control. 2021. Vol. 82, No.8. С. 1456-1462.

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