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

作者：Yan, Jiayuan; Zhang, Ding-Xue^*; Hu, Bin; Guan, Zhi-Hong; Chen, Guanrong; Cheng, Xin-Ming

来源：INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2022, 32(2): 567-582.

DOI：10.1002/rnc.5834

• controllability
• fixed point theorem
• impulsive effect
• nonlinear perturbation
• piecewise system

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.

• 单位
  华中科技大学