TY - JOUR

T1 - Uniform Ultimate Boundedness of Lur’e Systems with Switchings and Delays

AU - Андриянова, Наталья Романовна

PY - 2024/9/13

Y1 - 2024/9/13

N2 - The paper investigates a hybrid system consisting of Lur’e subsystems with constant delays and time-dependent switching. It is assumed that nonlinearities from the right side of the systems have degrees less than unity. An analysis of such a property of the system as the uniform ultimate boundedness of all its solutions is conducted. The linear part of the system is supposed to be asymptotically stable. As is known, this means that there is a correspondent homogeneous Lyapunov function. Using this function, a common Lyapunov–Krasovskii functional is constructed which makes it possible to find sufficient conditions for the uniform ultimate boundedness with arbitrary choices of positive delays and switching laws. Moreover, delays can occur during switching, for example, when generating feedback. The derived conditions are found to be less conservative in the case of asynchronous switching compared to synchronous ones. The validity of the theoretical results is confirmed through numerical modeling.

AB - The paper investigates a hybrid system consisting of Lur’e subsystems with constant delays and time-dependent switching. It is assumed that nonlinearities from the right side of the systems have degrees less than unity. An analysis of such a property of the system as the uniform ultimate boundedness of all its solutions is conducted. The linear part of the system is supposed to be asymptotically stable. As is known, this means that there is a correspondent homogeneous Lyapunov function. Using this function, a common Lyapunov–Krasovskii functional is constructed which makes it possible to find sufficient conditions for the uniform ultimate boundedness with arbitrary choices of positive delays and switching laws. Moreover, delays can occur during switching, for example, when generating feedback. The derived conditions are found to be less conservative in the case of asynchronous switching compared to synchronous ones. The validity of the theoretical results is confirmed through numerical modeling.

KW - равномерная предельная ограниченность решений

KW - запаздывание

KW - синхронное и асинхронное переключения

KW - asynchronous switching

KW - delay

KW - synchronous

KW - uniform ultimate boundedness

UR - https://www.mendeley.com/catalogue/f88ef593-f210-3e0a-b7a2-4d7823d18696/

U2 - 10.26516/1997-7670.2024.49.63

DO - 10.26516/1997-7670.2024.49.63

M3 - Article

VL - 49

SP - 63

EP - 77

JO - Bulletin of Irkutsk State University, Series Mathematics

JF - Bulletin of Irkutsk State University, Series Mathematics

SN - 1997-7670

ER -