Small-controllability of state-affine nonlinear systems

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2025-01-01 DOI:10.1016/j.jfranklin.2024.107437

Lingxiang Cheng, Lin Tie

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引用次数: 0

Abstract

This paper is concerned with the small-controllability problem of state-affine nonlinear systems, where the control inputs can be sufficiently small. By proposing the characteristic equation, a necessary condition for small-controllability of discrete-time state-affine nonlinear systems is first given, which covers the classical results for bilinear systems. The proposed characteristic equation is also generalized to continuous-time state-affine nonlinear systems. Then, two classes of sufficient conditions for small-controllability of discrete-time state-affine nonlinear systems are formulated by algebraizing the local rank condition. In this way, not only the classical sufficient results applied for the degenerate systems are improved, but also the scope is extended to more general state-affine nonlinear systems. Finally, the sufficient conditions are generalized to the multi-input case and the continuous-time case. Examples are given to illustrate the small-controllability results of this paper.

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来源期刊

Journal of The Franklin Institute-engineering and Applied Mathematics 工程技术-工程：电子与电气

CiteScore

7.30

自引率

14.60%

发文量

586

审稿时长

6.9 months

期刊介绍： The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.