474,906 research outputs found
A general stability criterion for feedback systems
Means for determining stability of feedback systems described by either linear or nonlinear differential equation
A general stability criterion for switched linear systems having stable and unstable subsystems
We report conditions on a switching signal that guarantee that solutions of a
switched linear systems converge asymptotically to zero. These conditions are
apply to continuous, discrete-time and hybrid switched linear systems, both
those having stable subsystems and mixtures of stable and unstable subsystems
A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks
This paper presents a stability test for a class of interconnected nonlinear
systems motivated by biochemical reaction networks. One of the main results
determines global asymptotic stability of the network from the diagonal
stability of a "dissipativity matrix" which incorporates information about the
passivity properties of the subsystems, the interconnection structure of the
network, and the signs of the interconnection terms. This stability test
encompasses the "secant criterion" for cyclic networks presented in our
previous paper, and extends it to a general interconnection structure
represented by a graph. A second main result allows one to accommodate state
products. This extension makes the new stability criterion applicable to a
broader class of models, even in the case of cyclic systems. The new stability
test is illustrated on a mitogen activated protein kinase (MAPK) cascade model,
and on a branched interconnection structure motivated by metabolic networks.
Finally, another result addresses the robustness of stability in the presence
of diffusion terms in a compartmental system made out of identical systems.Comment: See http://www.math.rutgers.edu/~sontag/PUBDIR/index.html for related
(p)reprint
On the stability of Hamiltonian relative equilibria with non-trivial isotropy
We consider Hamiltonian systems with symmetry, and relative equilibria with
isotropy subgroup of positive dimension. The stability of such relative
equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In
both papers the authors give sufficient conditions for stability which require
first determining a splitting of a subspace of the Lie algebra of the symmetry
group, with different splittings giving different criteria. In this note we
remove this splitting construction and so provide a more general and more
easily computed criterion for stability. The result is also extended to apply
to systems whose momentum map is not coadjoint equivariant
Enriched factorization systems
In a paper of 1974, Brian Day employed a notion of factorization system in
the context of enriched category theory, replacing the usual diagonal lifting
property with a corresponding criterion phrased in terms of hom-objects. We set
forth the basic theory of such enriched factorization systems. In particular,
we establish stability properties for enriched prefactorization systems, we
examine the relation of enriched to ordinary factorization systems, and we
provide general results for obtaining enriched factorizations by means of wide
(co)intersections. As a special case, we prove results on the existence of
enriched factorization systems involving enriched strong monomorphisms or
strong epimorphisms
Relativistic Dynamical Stability Criterion of Multi-Planet Systems with a Distant Companion
Multi-planetary systems are prevalent in our Galaxy. The long-term stability
of such systems may be disrupted if a distant inclined companion excites the
eccentricity and inclination of the inner planets via the eccentric Kozai-Lidov
mechanism. However, the star-planet and the planet-planet interactions can help
stabilize the system. In this work, we extend the previous stability criterion
that only considered the companion-planet and planet-planet interactions by
also accounting for short-range forces or effects, specifically, relativistic
precession induced by the host star. A general analytical stability criterion
is developed for planetary systems with inner planets and a relatively
distant inclined perturber by comparing precession rates of relevant dynamical
effects. Furthermore, we demonstrate as examples that in systems with and
inner planets, the analytical criterion is consistent with numerical
simulations using a combination of Gauss's averaging method and direct N-body
integration. Finally, the criterion is applied to observed systems,
constraining the orbital parameter space of a possible undiscovered companion.
This new stability criterion extends the parameter space in which an inclined
companion of multi-planet systems can inhabit.Comment: 16 pages, 10 figures, 3 tables, accepted by the Astrophysical Journa
On the stability of circular orbits in galactic dynamics: Newtonian thin disks
The study of off-equatorial orbits in razor-thin disks is still in its
beginnings. Contrary to what was presented in the literature in recent
publications, the vertical stability criterion for equatorial circular orbits
cannot be based on the vertical epicyclic frequency, because of the
discontinuity in the gravitational field on the equatorial plane. We present a
rigorous criterion for the vertical stability of circular orbits in systems
composed by a razor-thin disk surrounded by a smooth axially symmetric
distribution of matter, the latter representing additional structures such as
thick disk, bulge and (dark matter) halo. This criterion is satisfied once the
mass surface density of the thin disk is positive. Qualitative and quantitative
analyses of nearly equatorial orbits are presented. In particular, the analysis
of nearly equatorial orbits allows us to construct an approximate analytical
third integral of motion in this region of phase-space, which describes the
shape of these orbits in the meridional plane.Comment: 3 pages, 1 figure. In Proceedings of the MG13 Meeting on General
Relativity, Stockholm University, Sweden, 1-7 July 2012. World Scientific,
Singapore. Based on arXiv:1206.6501. in The Thirteenth Marcel Grossmann
Meeting: On Recent Developments in Theoretical and Experimental General
Relativity, Astrophysics, and Relativistic Field Theories (In 3 Volumes),
chap. 438, pages 2346-2348 (2015
μ-Dependent model reduction for uncertain discrete-time switched linear systems with average dwell time
In this article, the model reduction problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The stability criterion for general discrete-time switched systems is first explored, and a μ-dependent approach is then introduced for the considered systems to the model reduction solution. A reduced-order model is constructed and its corresponding existence conditions are derived via LMI formulation. The admissible switching signals and the desired reduced model matrices are accordingly obtained from such conditions such that the resulting model error system is robustly exponentially stable and has an exponential H∞ performance. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results
The inverse problem of the calculus of variations and the stabilization of controlled Lagrangian systems
We apply methods of the so-called `inverse problem of the calculus of
variations' to the stabilization of an equilibrium of a class of
two-dimensional controlled mechanical systems. The class is general enough to
include, among others, the inverted pendulum on a cart and the inertia wheel
pendulum. By making use of a condition that follows from Douglas'
classification, we derive feedback controls for which the control system is
variational. We then use the energy of a suitable controlled Lagrangian to
provide a stability criterion for the equilibrium
- …