Exponential stability analysis and control design for nonlinear system with time-varying delay

Xuelian Jin; Xuelian Jin

doi:10.3934/math.2021008

AIMS Mathematics

2021, Volume 6, Issue 1: 102-113. doi: 10.3934/math.2021008

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Research article

Exponential stability analysis and control design for nonlinear system with time-varying delay

Xuelian Jin ^,

College of Science, Liaoning University of Technology, Jinzhou, Liaoning, 121001, P. R. China

Received: 12 August 2020 Accepted: 24 September 2020 Published: 29 September 2020
MSC : 93B52, 93C42

This paper investigates the problem of exponential stability analysis and control design for time delay nonlinear systems with unknown control coefficient. Nussbaum gain function is utilized to solve the problem of unknown control directions at every step. By designing a new Lyapunov-Krasovskii functional, the problem of unknown time-varying delay is solved. Under the frame of adaptive backstepping recursive design, an exponential stabilization control algorithm is developed, which demonstrates that all solutions of controlled system are ultimately uniformly bounded (UUB) and exponential converge to zero. Finally, simulation results are displayed to explain the superiority and effectiveness of the developed control method.
- exponential stabilization,
- time-varying delay,
- Nussbaum gain function backstepping recursive design
Citation: Xuelian Jin. Exponential stability analysis and control design for nonlinear system with time-varying delay[J]. AIMS Mathematics, 2021, 6(1): 102-113. doi: 10.3934/math.2021008

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Abstract

This paper investigates the problem of exponential stability analysis and control design for time delay nonlinear systems with unknown control coefficient. Nussbaum gain function is utilized to solve the problem of unknown control directions at every step. By designing a new Lyapunov-Krasovskii functional, the problem of unknown time-varying delay is solved. Under the frame of adaptive backstepping recursive design, an exponential stabilization control algorithm is developed, which demonstrates that all solutions of controlled system are ultimately uniformly bounded (UUB) and exponential converge to zero. Finally, simulation results are displayed to explain the superiority and effectiveness of the developed control method.

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