Feedback stabilization of bifurcations in multivariable nonlinear systems - Part I: Equilibrium bifurcations

doi:10.1002/rnc.1134

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	Feedback stabilization of bifurcations in multivariable nonlinear systems - Part I: Equilibrium bifurcations
	Wang, Yong ; Murray, Richard M.
刊名	international journal of robust and nonlinear control
	2007
DOI	10.1002/rnc.1134
英文摘要	Under certain non-degeneracy conditions, necessary and sufficient conditions for stabilizability are obtained for multi-input nonlinear systems possessing a simple equilibrium bifurcation with the critical mode being linearly uncontrollable. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the bifurcation of the closed-loop system is a supercritical pitchfork bifurcation, which is equivalent to local asymptotic stability of the system at the bifurcation point. Stabilizability is reduced to the existence of solutions to a third order algebraic inequality, coupled with a quadratic algebraic equation, with the unknowns being the feedback gains. Explicit conditions for the existence of solutions to the algebraic equation and the inequality are derived. Part of the sufficient conditions are equivalent to the rank conditions of augmented matrices. Conditions under which there exists a stabilizing linear feedback law are also derived. The theoretical results are applied to active control of rotating stall in axial compressors using bleed valve as actuator. Copyright ? 2006 John Wiley & Sons, Ltd.; EI; 0; 4; 265-293; 17
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/410074]
专题	工学院
推荐引用方式 GB/T 7714	Wang, Yong,Murray, Richard M.. Feedback stabilization of bifurcations in multivariable nonlinear systems - Part I: Equilibrium bifurcations[J]. international journal of robust and nonlinear control,2007.
APA	Wang, Yong,&Murray, Richard M..(2007).Feedback stabilization of bifurcations in multivariable nonlinear systems - Part I: Equilibrium bifurcations.international journal of robust and nonlinear control.
MLA	Wang, Yong,et al."Feedback stabilization of bifurcations in multivariable nonlinear systems - Part I: Equilibrium bifurcations".international journal of robust and nonlinear control (2007).