Controllability analysis for a class of piecewise nonlinear impulsive non‐autonomous systems

This article investigates the controllability for a class of piecewise nonlinear impulsive non‐autonomous systems. The problem is addressed by considering the nonlinearities and impulses as perturbations. First, a standard framework is introduced to transform the issue of controllability to the exis...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2022-01, Vol.32 (2), p.567-582
Main Authors: Yan, Jiayuan, Zhang, Ding‐Xue, Hu, Bin, Guan, Zhi‐Hong, Chen, Guanrong, Cheng, Xin‐Ming
Format: Article
Language:English
Subjects:
Banach spaces
Controllability
fixed point theorem
Fixed points (mathematics)
impulsive effect
nonlinear perturbation
Nonlinearity
Perturbation
piecewise system
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Summary:This article investigates the controllability for a class of piecewise nonlinear impulsive non‐autonomous systems. The problem is addressed by considering the nonlinearities and impulses as perturbations. First, a standard framework is introduced to transform the issue of controllability to the existence of a fixed point by designing a proper admissible control and constructing a nonlinear operator on a Banach space. Then, two sufficient controllability conditions for such systems are developed by employing Schauder's and Rothe's fixed point theorems when the perturbations satisfy several nonlinear constraints including linear/sublinear growth conditions, bounded constraints, and Lipschitz conditions. It is shown that the controllability of such systems is influenced by the linear parts, the nonlinear perturbations, and the impulsive effects. Finally, the established controllability results are verified through several numerical examples.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.5834