Finite-Time Stability and High Relative Degrees in Sliding-Mode Control

2011 ◽  
pp. 59-92 ◽  
Author(s):  
Arie Levant
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Time Stability ◽  
Finite Time Stability ◽  
Mode Control

Chattering-Free Finite-Time Stability of a Class of Fractional-Order Nonlinear Systems

2019 ◽  
Author(s):  
Bin Wang ◽  
Yangquan Chen ◽  
Ying Yang
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Time Stability ◽  
External Disturbances ◽  
Finite Time Stability ◽  
Mode Control ◽  
Chattering Free

Abstract This paper studies the chattering-free finite-time control for a class of fractional-order nonlinear systems. First, a class of fractional-order nonlinear systems with external disturbances is presented. Second, a new finite-time terminal sliding mode control method is proposed for the stability control of a class of fractional-order nonlinear systems by combining the finite-time stability theory and sliding mode control scheme. Third, by designing a controller with a differential form and introducing the arc tangent function, the chattering phenomenon is well suppressed. Additionally, a controller is developed to resist external disturbances. Finally, numerical simulations are implemented to demonstrate the feasibility and validity of the proposed method.

scholarly journals Finite time stability and sliding mode control for uncertain variable fractional order nonlinear systems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jingfei Jiang ◽  
Hongkui Li ◽  
Kun Zhao ◽  
Dengqing Cao ◽  
Juan L. G. Guirao
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Direct Method ◽  
Uncertain Variable ◽  
Time Stability ◽  
Finite Time Stability ◽  
Mode Control

AbstractThis paper deals with the finite time stability and control for a class of uncertain variable fractional order nonlinear systems. The variable fractional Lyapunov direct method is developed to provide the basis for the stability proof of the system considered. The sliding mode control method is applied for robust control of uncertain variable fractional order systems; furthermore, the chattering phenomenon is avoided. And the finite time stability of the systems under control law is proved based on the proposed stability criterion. Finally, numerical simulations are proposed and the efficiency of the controller is verified.

A finite-time sliding mode control for hypersonic vehicle

2019 ◽  
Vol 41 (15) ◽  
pp. 4339-4350 ◽  
Author(s):  
Qingwen Ma ◽  
Jianguo Guo ◽  
Jun Zhou
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Hypersonic Vehicle ◽  
Lyapunov Theory ◽  
Terminal Sliding Mode ◽  
Finite Time Stability ◽  
Mode Control ◽  
Time Control ◽  
Longitudinal Dynamic

In this paper, a finite-time control strategy based on back-stepping method combining with a terminal sliding mode control (TSMC) and a nonlinear disturbance observer (NDO) is proposed for the longitudinal dynamic model of hypersonic vehicle (HV). Firstly, the model of HV is transformed into two strict feedback subsystem: the mismatched subsystem of altitude and the matched subsystem of velocity. Then, the TSMC and back-stepping method is incorporated to cope with the unmatched issue in the HV altitude subsystem. In addition, a NDO based on a finite-time-convergent differentiator (FD) is proposed to estimate the lumped disturbances. The finite-time stability condition of the system is established via the Lyapunov theory. Finally, the robustness and effectiveness of the method are verified by simulations.

scholarly journals DHMM-Based Asynchronous Finite-Time Sliding Mode Control for Markovian Jumping Lur’e Systems

2021 ◽  
Author(s):  
Rong NIE ◽  
Wenli DU ◽  
Zhongmei LI ◽  
Zhao ZHOU ◽  
Shuping HE
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Sliding Surface ◽  
Integral Type ◽  
Lur’E Systems ◽  
Markovian Jumping ◽  
Finite Time Stability ◽  
Mode Control ◽  
Sliding Mode Dynamics

Abstract This paper is concerned with the asynchronous problem for a class of Markovian jumping Lur’s system (MJLSs) via sliding mode control (SMC) in continuous-time domain. Specifically, the discrete hidden Markovian model (DHMM) is employed to describe the nonsynchronization between the controller modes and the MJLSs modes. In particular, considering the nonlinearity of MJLSs, a novel Lur’e-integral-type sliding surface is constructed. In order to ensure the finite-time stability of sliding mode dynamics and the accessibility of the specified sliding surface, the asynchronous Lur’e-type SMC law of the detector mode is presented. Finally, an example of DC motor is provided to demonstrate the effectiveness of the proposed technique.

Sign in / Sign up

Export Citation Format

Share Document