Finite-time sliding mode control for uncertain singular systems with one-side Lipschitz nonlinearities and time-varying delays

This paper primarily focused on a finite-time sliding mode control (SMC) problem for uncertain singular systems with OSL nonlinearities. Under the condition of a suitable SMC law, a time-division strategy is used to divide the time interval [0,  T ] into two phases, which are the arrival phase [ 0 ,...

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Bibliographic Details
Published in:Computational & applied mathematics 2024-03, Vol.43 (2), Article 96
Main Authors: Han, Fengying, Yang, Dongmei, Ren, Junchao
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Control systems
Linear matrix inequalities
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Nonlinearity
Sliding mode control
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Summary:This paper primarily focused on a finite-time sliding mode control (SMC) problem for uncertain singular systems with OSL nonlinearities. Under the condition of a suitable SMC law, a time-division strategy is used to divide the time interval [0,  T ] into two phases, which are the arrival phase [ 0 , T ∗ ] and the sliding motion phase [ T ∗ , T ] , respectively. Firstly, it is proved that the time T ∗ to reach the sliding mode surface is less than T . Secondly, it is proved that uncertain singular systems with OSL nonlinearities are regular and impulse-free. Whereafter, the related conditions are derived to guarantee that the system satisfies singular sliding mode finite-time boundedness (SSMFTB) during the whole phase [0,  T ]. Next, the controller and observer gain matrices can be computed in term of the linear matrix inequality (LMI) method. Lastly, numerical examples are presented to demonstrate the effectiveness of the proposed new design schemes.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-023-02464-x