Results 1  10
of
2,100
Finitetime stability of homogeneous systems,”
 in Proceedings of the American Control Conference,
, 1997
"... Abstract This paper examines finitetime stability of homogeneous systems. The main result is that a homogeneous system is finitetime stable if and only if it is asymptotically stable and has a negative degree of homogeneity. ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
Abstract This paper examines finitetime stability of homogeneous systems. The main result is that a homogeneous system is finitetime stable if and only if it is asymptotically stable and has a negative degree of homogeneity.
Decentralized FiniteTime Stabilizing Feedback Network Control
, 2012
"... This work explores the stability properties of a class of nonlinear system, which is obtained by applying a special transformation to the vector field of a linear system. It is proved that such a nonlinear system preserves the stability of the original linear system. This property can be used for ch ..."
Abstract
 Add to MetaCart
for checking the stability of certain nonlinear systems, and designing novel network control protocols based on homogeneous system theory. For the network control application, finitetime convergence can be achieved in a decentralized manner by properly choosing the smooth feedback control law. The results
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
 Proceedings of the National Academy of Sciences
, 2005
"... of contexts of data analysis, such as spectral graph theory, manifold learning, nonlinear principal components and kernel methods. We augment these approaches by showing that the diffusion distance is a key intrinsic geometric quantity linking spectral theory of the Markov process, Laplace operators ..."
Abstract

Cited by 257 (45 self)
 Add to MetaCart
operators, or kernels, to the corresponding geometry and density of the data. This opens the door to the application of methods from numerical analysis and signal processing to the analysis of functions and transformations of the data. Abstract. We provide a framework for structural multiscale geometric
Geometric Homogeneity with Applications to
, 2004
"... This paper studies properties of homogeneous systems in a geometric, coordinatefree setting. A key contribution of this paper is a result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin. This result makes i ..."
Abstract
 Add to MetaCart
it possible to extend previous results on homogeneous systems to the geometric framework. As an application of our results, we consider ¯nitetime stability of homogeneous systems. The main result that links homogeneity and ¯nitetime stability is that a homogeneous system is ¯nitetime stable if and only
Finitetime convergent gradient flows with applications to network consensus
 Automatica
"... This paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function. Extending recent results on nonsmooth stability analysis, we characterize their asymptotic convergence properties and identify conditions that guarantee finitetime convergence. We d ..."
Abstract

Cited by 66 (5 self)
 Add to MetaCart
This paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function. Extending recent results on nonsmooth stability analysis, we characterize their asymptotic convergence properties and identify conditions that guarantee finitetime convergence. We
Linearization of hyperbolic finitetime processes
 J. Diff. Equations
"... We adapt the notion of processes to introduce an abstract framework for dynamics in finite time, i.e. on compact time sets. For linear finitetime processes a notion of hyperbolicity namely exponential monotonicity dichotomy (EMD) is introduced, thereby generalizing and unifying several existing app ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
of linearizations of finitetime processes, including finitetime analogues of the local (un)stable manifold theorem and theorem of linearized asymptotic stability. As an application, we discuss our results for ordinary differential equations on a compact timeinterval.
Oscillatory finitetime singularities in finance, population and rupture
 PHYSICA A
, 2002
"... We present a simple twodimensional dynamical system where two nonlinear terms, exerting respectively positive feedback and reversal, compete to create a singularity in finite time decorated by accelerating oscillations. The power law singularity results from the increasing growth rate. The oscillat ..."
Abstract

Cited by 24 (12 self)
 Add to MetaCart
We present a simple twodimensional dynamical system where two nonlinear terms, exerting respectively positive feedback and reversal, compete to create a singularity in finite time decorated by accelerating oscillations. The power law singularity results from the increasing growth rate
Application of FiniteTime Stability Concepts to the Control of ATM Networks
, 2003
"... When dealing with the stability of a system, a distinction should be made between classical Lyapunov Stability and FiniteTime Stability (FTS) (or ShortTime Stability). The concept of Lyapunov Asymptotic Stability is largely known ..."
Abstract
 Add to MetaCart
When dealing with the stability of a system, a distinction should be made between classical Lyapunov Stability and FiniteTime Stability (FTS) (or ShortTime Stability). The concept of Lyapunov Asymptotic Stability is largely known
Generalized principal component analysis (GPCA)
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... This paper presents an algebrogeometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a ..."
Abstract

Cited by 206 (36 self)
 Add to MetaCart
This paper presents an algebrogeometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives
Geometric Homogeneity And Stabilization
 In Preprints of IFAC Nonlinear Control Systems Design Symposium (NOLCOS'95
, 1995
"... . We present a consistent, geometric notion of homogeneity, for vector fields (differential equations and control systems), functions, differential forms and endomorphisms. The fundamental observation is that homogeneity is an intrinsic, geometric property. Accordingly, a coordinatefree characte ..."
Abstract
 Add to MetaCart
. We present a consistent, geometric notion of homogeneity, for vector fields (differential equations and control systems), functions, differential forms and endomorphisms. The fundamental observation is that homogeneity is an intrinsic, geometric property. Accordingly, a coordinate
Results 1  10
of
2,100