Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(2): 527-536

https://doi.org/10.1007/s12555-022-1184-3

© The International Journal of Control, Automation, and Systems

General Stabilization for Stochastic System With Input Delay and Multiplicative Noise: Continuous-time Case

Cheng Tan*, Jianying Di, Zhengqiang Zhang, and Wing Shing Wong

Qufu Normal University

Abstract

This paper investigates the general stabilization issues for continuous-time stochastic dynamics whose input delay and multiplicative noise in control variable exist simultaneously. On the one hand, we present a set of necessary and sufficient conditions for stabilizing the considered stochastic dynamics in mean-square sense. Different from many previous works, one significant innovation is that our control policy is designed as the feedback of an extended state that contains the current available state and some past control information. On the other hand, another important innovation is that we for the first time generalize the notions of critical stabilization and essential destabilization to stochastic time-delay model in terms of spectral analysis technique, while the related necessary and sufficient stabilization conditions are derived respectively.

Keywords Asymptotic mean-square stabilization, critical stabilization, delay-dependent Lyapunov operator, essential destabilization, spectrum.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(2): 527-536

Published online February 1, 2024 https://doi.org/10.1007/s12555-022-1184-3

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

General Stabilization for Stochastic System With Input Delay and Multiplicative Noise: Continuous-time Case

Cheng Tan*, Jianying Di, Zhengqiang Zhang, and Wing Shing Wong

Qufu Normal University

Abstract

This paper investigates the general stabilization issues for continuous-time stochastic dynamics whose input delay and multiplicative noise in control variable exist simultaneously. On the one hand, we present a set of necessary and sufficient conditions for stabilizing the considered stochastic dynamics in mean-square sense. Different from many previous works, one significant innovation is that our control policy is designed as the feedback of an extended state that contains the current available state and some past control information. On the other hand, another important innovation is that we for the first time generalize the notions of critical stabilization and essential destabilization to stochastic time-delay model in terms of spectral analysis technique, while the related necessary and sufficient stabilization conditions are derived respectively.

Keywords: Asymptotic mean-square stabilization, critical stabilization, delay-dependent Lyapunov operator, essential destabilization, spectrum.

IJCAS
February 2024

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

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