Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(2): 571-580

https://doi.org/10.1007/s12555-022-1026-3

© The International Journal of Control, Automation, and Systems

Global Exponential Robust Stability of Generalized Differential Dynamical System With Deviating Argument and Random Disturbance

Yueli Huang and Ailong Wu*

Hubei Normal University

Abstract

In this paper, we analyze robust stability of differential dynamical system with deviating argument in derivative part. By using inequality technique and stochastic analysis idea, we obtain the upper bounds of the interval length of deviating argument and the noise intensity, respectively. First, it is proved theoretically that for a given exponentially stable differential dynamical system (DDS), if the interval length of deviating argument is lower than the upper bound, DDS with deviating argument will still maintain exponentially stable. In addition, it is also proved that for a given exponentially stable DDS, if the interval length of deviating argument and noise intensity are lower than the upper bound, stochastic DDS (SDDS) with deviating argument will remain exponentially stable. Finally, theoretical findings are supported by two examples.

Keywords Deviating argument, differential dynamical system, random disturbance, robust stability.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(2): 571-580

Published online February 1, 2024 https://doi.org/10.1007/s12555-022-1026-3

Copyright © The International Journal of Control, Automation, and Systems.

Global Exponential Robust Stability of Generalized Differential Dynamical System With Deviating Argument and Random Disturbance

Yueli Huang and Ailong Wu*

Hubei Normal University

Abstract

In this paper, we analyze robust stability of differential dynamical system with deviating argument in derivative part. By using inequality technique and stochastic analysis idea, we obtain the upper bounds of the interval length of deviating argument and the noise intensity, respectively. First, it is proved theoretically that for a given exponentially stable differential dynamical system (DDS), if the interval length of deviating argument is lower than the upper bound, DDS with deviating argument will still maintain exponentially stable. In addition, it is also proved that for a given exponentially stable DDS, if the interval length of deviating argument and noise intensity are lower than the upper bound, stochastic DDS (SDDS) with deviating argument will remain exponentially stable. Finally, theoretical findings are supported by two examples.

Keywords: Deviating argument, differential dynamical system, random disturbance, robust stability.

IJCAS
February 2024

Vol. 22, No. 2, pp. 347~729

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IJCAS

eISSN 2005-4092
pISSN 1598-6446