Third-order nilpotency, nice reachability and asymptotic stability

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:233

Article

Sharon, Yoav ; Margaliot, Michael

关键词: nonlinear switched systems;    arbitrary switching;    global asymptotic stability;    optimal control;    first- and second-order maximum principle;    bang-bang control;    singular control;    lie bracket;    P. Hall basis;    Sussmann's product expansion;    Chen series;   

DOI  :  10.1016/j.jde.2006.10.011

来源: Elsevier

【 摘 要 】

We consider an affine control system whose vector fields span a third-order nilpotent Lie algebra. We show that the reachable set at time T using measurable controls is equivalent to the reachable set at time T using piecewise-constant controls with no more than four switches. The bound on the number of switches is uniform over any final time T. As a corollary, we derive a new sufficient condition for stability of nonlinear switched systems under arbitrary switching. This provides a partial solution to an open problem posed in [D. Liberzon, Lie algebras and stability of switched nonlinear systems, in: V. Blonde], A. Megretski (Eds.), Unsolved Problems in Mathematical Systems and Control Theory, Princeton Univ. Press, 2004, pp. 203207]. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free