### AIMS Mathematics

2021, Issue 1: 102-113. doi: 10.3934/math.2021008
Research article

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

• 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.

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

### Related Papers:

• 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.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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