Journal ArticleDOI
Homogeneous Lyapunov function for homogeneous continuous vector field
TLDR
In this article, a construction of a homogeneous Lyapunov function P associated with a system of differential equations J = f(x), x ~ R ~ (n > 1), under the hypotheses: (1) f ~ C(R n, ~) vanishes at x = 0 and is homogeneous; (2) the zero solution of this system is locally asymptotically stable.About:
This article is published in Systems & Control Letters.The article was published on 1992-12-01. It has received 720 citations till now.read more
Citations
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Journal ArticleDOI
Higher-order sliding modes, differentiation and output-feedback control
TL;DR: In this article, the authors proposed arbitrary-order robust exact differentiators with finite-time convergence, which can be used to keep accurate a given constraint and feature theoretically-infinite-frequency switching.
Journal ArticleDOI
Small-gain theorem for ISS systems and applications
TL;DR: This work addresses the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.
Journal ArticleDOI
Geometric homogeneity with applications to finite-time stability
TL;DR: A result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin makes it possible to extend previous results on homogeneous systems to the geometric framework.
Journal ArticleDOI
A continuous feedback approach to global strong stabilization of nonlinear systems
Chunjiang Qian,Wei Lin +1 more
TL;DR: Conditions under which it is possible to prove the existence of continuous state feedback control laws that achieve global strong stability (GSS) in the sense of Kurzweil (1956) are described.
Journal ArticleDOI
Global finite-time stabilization of a class of uncertain nonlinear systems
Xianqing Huang,Wei Lin,Bo Yang +2 more
TL;DR: It is proved that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system can be achieved by Holder continuous state feedback.
References
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Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Journal ArticleDOI
Adding an integrator for the stabilization problem
Jean-Michel Coron,Lorent Praly +1 more
TL;DR: In this article, the authors studied the relationship between the following two properties: P1: the system x = f(x, y), y = v is locally asymptotically stabilizable; and P2: the systems x = r n, y ϵ R, r n, r r, r r is locally stabilizable, where r n is the dimension of the system.
Journal ArticleDOI
Stabilization of nonlinear systems in the plane
TL;DR: In this paper, it was shown that every small-time locally controllable system in the plane can be asymptotically stabilized by employing locally Holder continuous feedback laws, as essentially was conjectured by E. Sontag.