Polytope joint Lyapunov functions for positive LSS

Авторы: Guglielmi N., Laglia L., Protasov V.Yu
Сборник: Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on
Год издания: 2014
Место издания: IEEE Conference Publications
Первая страница: 710
Последняя страница: 715
DOI: 10.1109/CDC.2013.6759965
Аннотация: We consider switched linear systems of odes, ẋ x(t)= A(u(t))x(t) where A(u(t)) ∈ A, a compact set of matrices. In this paper we propose a new method for the approximation of the upper Lyapunov exponent and lower Lyapunov exponent of the LSS when the matrices in A are Metzler matrices (or the generalization of them for arbitrary cone), arising in many interesting applications (see e.g. [9]). The method is based on the iterative construction of invariant positive polytopes for a sequence of discretized systems obtained by forcing the switching instants to be multiple of Δ(k)t where Δ(k)t → 0 as k → ∞. These polytopes are then used to generate a monotone piecewise-linear joint Lyapunov function on the positive orthant, which gives tight upper and lower bounds for the Lyapunov exponents. As a byproduct we detect whether the considered system is stabilizable or uniformly stable. The efficiency of this approach is demonstrated in numerical examples, including some of relatively large dimensions.
Добавил в систему: Протасов Владимир Юрьевич

	ИСТИНА	Войти в систему Регистрация
	Интеллектуальная Система Тематического Исследования НАукометрических данных
	Главная Поиск Статистика О проекте Помощь

ИСТИНА