947 research outputs found
Stability of uniformly bounded switched systems and Observability
This paper mainly deals with switched linear systems defined by a pair of
Hurwitz matrices that share a common but not strict quadratic Lyapunov
function. Its aim is to give sufficient conditions for such a system to be
GUAS.We show that this property of being GUAS is equivalent to the uniform
observability on of a bilinear system defined on a subspace whose
dimension is in most cases much smaller than the dimension of the switched
system.Some sufficient conditions of uniform asymptotic stability are then
deduced from the equivalence theorem, and illustrated by examples.The results
are partially extended to nonlinear analytic systems
Algebraic stability analysis of constraint propagation
The divergence of the constraint quantities is a major problem in
computational gravity today. Apparently, there are two sources for constraint
violations. The use of boundary conditions which are not compatible with the
constraint equations inadvertently leads to 'constraint violating modes'
propagating into the computational domain from the boundary. The other source
for constraint violation is intrinsic. It is already present in the initial
value problem, i.e. even when no boundary conditions have to be specified. Its
origin is due to the instability of the constraint surface in the phase space
of initial conditions for the time evolution equations. In this paper, we
present a technique to study in detail how this instability depends on gauge
parameters. We demonstrate this for the influence of the choice of the time
foliation in context of the Weyl system. This system is the essential
hyperbolic part in various formulations of the Einstein equations.Comment: 25 pages, 5 figures; v2: small additions, new reference, publication
number, classification and keywords added, address fixed; v3: update to match
journal versio
Extension of germs of holomorphic foliations
We consider the problem of extending germs of plane holomorphic foliations to
foliations of compact surfaces. We show that the germs that become regular
after a single blow up and admit meromorphic first integrals can be extended,
after local changes of coordinates, to foliations of compact surfaces. We also
show that the simplest elements in this class can be defined by polynomial
equations. On the other hand we prove that, in the absence of meromorphic first
integrals there are uncountably many elements without polynomial
representations.Comment: 17 page
Good Reduction for Endomorphisms of the Projective Line in Terms of the Branch Locus
Let be a number field and a non archimedean valuation on . We say
that an endomorphism has good
reduction at if there exists a model for such that
, the degree of the reduction of modulo , equals
and is separable. We prove a criterion for good reduction
that is the natural generalization of a result due to Zannier in \cite{Uz3}.
Our result is in connection with other two notions of good reduction, the
simple and the critically good reduction. The last part of our article is
dedicated to prove a characterization of the maps whose iterates, in a certain
sense, preserve the critically good reduction.Comment: 23 pages, comments are welcom
The stability interval of the set of linear system
The article considers the problem of stability of interval-defined linear systems based on the Hurwitz and Lienard-Shipar interval criteria. Krylov, Leverier, and Leverier-Danilevsky algorithms are implemented for automated construction and analysis of the interval characteristic polynomial. The interval mathematics library was used while developing the software. The stability of the dynamic system described by linear ordinary differential equations is determined and based on the properties of the eigenvalues of the interval characteristic polynomial. On the basis of numerical calculations, the authors compare several methods of constructing the characteristic polynomial. The developed software that implements the introduced interval arithmetic operations can be used in the study of dynamic properties of automatic control systems, energy, economic and other non-linear systems
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