Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(2): 560-570

https://doi.org/10.1007/s12555-022-0579-5

© The International Journal of Control, Automation, and Systems

Delay Feedback Control Based on Discrete-time State Observations for Highly Nonlinear Hybrid Stochastic Functional Differential Equations With Infinite Delay

Lei Zhao* and Qiuqiu Fan*

Harbin Institute of Technology

Abstract

In this paper, it is proved that an unstable highly nonlinear hybrid stochastic functional differential equation with infinite delay (HNHISFDE) can be stabilized by designing a controller that not only depends on discretetime state observations, but only produces different time lags in each observation. Firstly, common conditions are imposed on the original system to ensure the existence and uniqueness of the solution. Secondly, the design method of delay feedback control is presented to stabilize a class of HNHISFDEs. Notably, new assumptions based on Lyapunov functional and M-matrix methods are provided to construct the controller step by step. Then, the sufficient criteria of H∞ stabilization, asymptotic stabilization and exponential stabilization are established by applying the Lyapunov stability theory. Finally, the effectiveness of the theoretical results is illustrated by a numerical example.

Keywords Discrete-time state feedback, highly nonlinear system, infinite delay, Lyapunov functional, stabilization.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(2): 560-570

Published online February 1, 2024 https://doi.org/10.1007/s12555-022-0579-5

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

Delay Feedback Control Based on Discrete-time State Observations for Highly Nonlinear Hybrid Stochastic Functional Differential Equations With Infinite Delay

Lei Zhao* and Qiuqiu Fan*

Harbin Institute of Technology

Abstract

In this paper, it is proved that an unstable highly nonlinear hybrid stochastic functional differential equation with infinite delay (HNHISFDE) can be stabilized by designing a controller that not only depends on discretetime state observations, but only produces different time lags in each observation. Firstly, common conditions are imposed on the original system to ensure the existence and uniqueness of the solution. Secondly, the design method of delay feedback control is presented to stabilize a class of HNHISFDEs. Notably, new assumptions based on Lyapunov functional and M-matrix methods are provided to construct the controller step by step. Then, the sufficient criteria of H∞ stabilization, asymptotic stabilization and exponential stabilization are established by applying the Lyapunov stability theory. Finally, the effectiveness of the theoretical results is illustrated by a numerical example.

Keywords: Discrete-time state feedback, highly nonlinear system, infinite delay, Lyapunov functional, stabilization.

IJCAS
February 2024

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

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eISSN 2005-4092
pISSN 1598-6446