A Characterization of Normal Forms for Control Systems
نویسندگان
چکیده
منابع مشابه
Normal Forms of Nonlinear Control Systems
Numerous papers were published during the last decade on the normal forms of nonlinear control systems with applications in bifurcation and its control. The approach is motivated by Poincaré’s theory of normal forms for classical dynamical systems using homogeneous transformations. In this paper, we summarize a variety of control system normal forms published in the literature so that the norma...
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Consider a Dynamical system x'=F(x,µ) such that its linear part has a pair of imaginary eigenvalues and one zero eigenvalue (Hopf zero singularity). Recently, the simplest normal form for this singular system has been obtained by sl(2) Lie algebra theory and the decomposition of space into three invariant subspaces. The normal form of this singular system is divided into three general cases. In...
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A fruitful technique for the local analysis of a dynamical system consists of using a local change of coordinates to transform the system to a simpler form, which is called a normal form. The qualitative behavior of the original system is equivalent to that of its normal form which may be easier to analyze. A bifurcation of a parameterized dynamics occurs when a change in the parameter leads to...
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This paper addresses the problem of bifurcation analysis for nonlinear control systems. It is a review of some results published in recent years on bifurcations of control systems based on the normal form approach. We address three problems for systems with a single uncontrollable mode, namely the problem of normal forms, bifurcations of control systems, and bifurcation control by state feedback.
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The quadratic and cubic normal forms of discrete time nonlinear control systems are presented. These are the normal forms with respect to the group of state coordinate changes and invertible state feedbacks. We introduce the concept of a control bifurcation for such systems. A control bifurcation takes place at an equilibrium where there is a loss of linear stabilizability in contrast to a clas...
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ژورنال
عنوان ژورنال: Journal of Dynamical and Control Systems
سال: 2014
ISSN: 1079-2724,1573-8698
DOI: 10.1007/s10883-014-9264-1