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A dynamical system which must be stable whose stability cannot be proved

2004
*
Theoretical Computer Science
*

to the correctness of ZF set theory-

doi:10.1016/j.tcs.2004.05.001
fatcat:nf4awspykvdkbp3fwz7kmzzgpy
*a*property*which**must**be*assumed to hold but*which**cannot**be**proved*within ZF. ... Building on*a*result of Blondel, we show that there exists*a*piecewise*a*ne*dynamical**system**whose**stability*(local asymptotic*stability*, global asymptotic*stability*and global convergence) is equivalent ... They then show that such*a*theory*cannot*successfully encapsulate our notion of truth-there are*systems**which*are truly*stable**which*we*cannot**prove*to*be**stable*. ...##
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A sufficient condition for stability of a polytope of matrices

1994
*
Systems & control letters (Print)
*

The results developed can also

doi:10.1016/0167-6911(94)90045-0
fatcat:poqp7naonfecpms6hvs5eguk6i
*be*applied to the*stability*of*a*positive cone of matrices and sufficient conditions for the*stability*of interval*dynamical**systems*are obtained. ...*A*sufficient condition for the*stability*of*a*polytope of matrices,*which*is shown to*be*necessary and sufficient for*a*certain class of matrices, is obtained. ... In his short paper, Kharitonov [12]*proved*that the*stability*of*dynamical**systems**whose*parameter uncertainty is restricted to*a*rectangular domain is guaranteed by the*stability*of properly chosen ...##
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Stability of Real Parametric Polynomial Discrete Dynamical Systems

2015
*
Discrete Dynamics in Nature and Society
*

The exact boundary values of these

doi:10.1155/2015/680970
fatcat:wjpktuxpbvha3nu4snjwpreox4
*stability*bands are yet to*be*calculated for regions of type greater than one for polynomials of degree higher than three. ... We extend and improve the existing characterization of the*dynamics*of general quadratic real polynomial maps with coefficients that depend on*a*single parameterλand generalize this characterization to ... Although the*dynamics*of parametric polynomial discrete*systems*are very complex their bifurcation diagrams have*proved*to*be**a*very useful visual tool. ...##
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Codimension one generic homoclinic classes with interior

2010
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Bulletin of the Brazilian Mathematical Society
*

We study generic diffeomorphisms

doi:10.1007/s00574-010-0006-z
fatcat:7qexfa5awna6fddmgdckndd5nu
*whose*nonwandering set has interior. Under some assumptions on the*dynamics*of the derivative of the diffeomorphims we*prove*that it should*be*transitive. ... This has some interesting consequences, mainly in low dimensional*systems*. ... To do this we use Lyapunov*stability*of the class and the Lemma of Liao*which*gives uniform size on the*stable*and unstable sets of the periodic points we find and thus we*prove*the theorem. ...##
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Output-input stability and minimum-phase nonlinear systems

2002
*
IEEE Transactions on Automatic Control
*

The class of output-input

doi:10.1109/9.989070
fatcat:luwuhhdyijbw7essxiwerlihie
*stable**systems*thus defined includes all affine*systems*in global normal form*whose*internal*dynamics*are input-to-state*stable*and also all left-invertible linear*systems**whose*... The definition of output-input*stability*does not rely on*a*particular choice of coordinates in*which*the*system*takes*a*normal form or on the computation of zero*dynamics*. ... The class of output-input*stable**systems*thus defined includes all affine*systems*in global normal form*whose*internal*dynamics*are input-to-state*stable*and also all left-invertible linear*systems**whose*...##
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Page 5285 of Mathematical Reviews Vol. , Issue 97H
[page]

1997
*
Mathematical Reviews
*

In particular, normal form theory for Hamiltonian

*systems*is used to argue that generic (elliptic) fixed points of the*system**cannot**be**stable*. ... The*stability*of learning*must*therefore*be*analyzed for the entire*system*of individuals’ strategy adjustments. ...##
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Complexity of Ten Decision Problems in Continuous Time Dynamical Systems
[article]

2012
*
arXiv
*
pre-print

of

arXiv:1210.7420v1
fatcat:25m44ydiobdqdlxzn3c7qarlty
*systems*and control theory*cannot*have*a*polynomial time (or even pseudo-polynomial time) algorithm unless P=NP: local attractivity of an equilibrium point,*stability*of an equilibrium point in the ...*a*quartic semialgebraic set under linear*dynamics*, local collision avoidance, and existence of*a**stabilizing*control law. ... Then, we have shown while*proving*(e) that (2)*must*also*be*las and hence*stable*in the sense of Lyapunov. ...##
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Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm

2002
*
IEEE Transactions on Automatic Control
*

For example, for

doi:10.1109/tac.2002.803542
fatcat:nraxgqh5qvc2hn23lymernj2ru
*a*class of detectable bilinear*systems*[4] or affine and nonaffine*systems*with*stable*-free*dynamics*[9] , [10] , global*stabilization*via output feedback was*proved*to*be*solvable ... CONCLUSION We have presented*a*new output feedback control scheme for*a*class of nonlinear*systems**whose*global*stabilization*problem via output feedback*cannot**be*handled by existing methods. ...##
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Noninteracting Control with Stability for Hamiltonian Systems

1998
*
IFAC Proceedings Volumes
*

The problem of noninteraction with

doi:10.1016/s1474-6670(17)40368-5
fatcat:mbe3o3i5qnhgfptsocjxy42qim
*stability*via*dynamic*state feedback is addressed and solved for*a*class of nonlinear Hamiltonian*systems*. ... It is well known that to decide if the problem is solvable, and*which*class of state feedback has to*be*used, the*stability*properties of some special*dynamics*are to*be*investigated. ... On the contrary, since the zero*dynamics*(18) are clearly unstable, the*system**cannot**be*rendered noninteractive and*stable*with*a*PD-type decentralized control law. ...##
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State feedback impulsive therapy to SIS model of animal infectious diseases

2019
*
Physica A: Statistical Mechanics and its Applications
*

Basing on the impulsive model, the existence of order-1 periodic solution and its

doi:10.1016/j.physa.2018.09.161
pmid:32288107
pmcid:PMC7126221
fatcat:d53a6xan6vef7nialzepwu7wqm
*stability*are*proved*with*a*novel method. ...*A*state feedback impulsive model is constructed to depict the transmission and treatment of animal epidemics. ... First, we*prove*that in the first quadrant the line*whose*slope is −1*cannot**be*tangent with any trajectory of*system*(1.1). ...##
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Synchronization in On-Off Stochastic Networks: Windows of Opportunity

2015
*
IEEE Transactions on Circuits and Systems Part 1: Regular Papers
*

We apply

doi:10.1109/tcsi.2015.2415172
fatcat:7re2753gafg6vantkbqi2khhte
*a*recently developed general theory of blinking*systems*to*prove*global*stability*of synchronization in the fast switching limit. ... We study*dynamical*networks*whose*topology and intrinsic parameters stochastically change, on*a*time scale that ranges from fast to slow. ... Hence, there are trajectories that escape to infinity, and the existence of the global absorbing domain*cannot**be**proved*. ...##
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Instability, Modus ponens and uncertainty of deduction

2006
*
Frontiers of Philosophy in China
*

Some kind of

doi:10.1007/s11466-006-0030-7
fatcat:565f4fiwenasncavwvydchpfim
*stability*hypothesis should*be*added in order to draw meaningful conclusion. ... cause*cannot*gain similar result. ... No matter how to define the terms, chaotic phenomena are*proved*in many important*dynamical*processes, and for these*system*complicated*stabilities**must**be*studied carefully. ...##
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Generalized proportional-plus-derivative compensators for a class ofuncertain plants

1991
*
Journal of Guidance Control and Dynamics
*

For the present problem, to

doi:10.2514/3.20693
fatcat:r5uawmzwpvdcblu2fhfjhlos6e
*prove*the*stability*, we shall assume that PC has no unstable cancellations. The*stability*of G(s) would then*be*sufficient to*prove*the*stability*of the*system*. ... Therefore, Eq. (8)*cannot**be*true for any real w, and D,(s) is Hurwitz, i.e., G, is*stable*. ...##
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Stability regions of nonlinear autonomous dynamical systems

1988
*
IEEE Transactions on Automatic Control
*

*A*topological and

*dynamical*characterization of the

*stability*boundaries for

*a*fairly large class of nonlinear autonomous

*dynamic*

*systems*is presented. ... The

*stability*boundary of

*a*

*stable*equilibrium point is shown to consist of the

*stable*manifolds of all the equilibrium points (and/or closed orbits) on the

*stability*boundary. ... Now, consider two cases.

*a*) h = 1: Then m

*must*

*be*zero (i.e., 2

*must*

*be*

*a*

*stable*equilibrium point),

*which*is

*a*contradiction to the fact that no

*stable*equilibrium point exists on the

*stability*boundary ...

##
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Page 1583 of American Society of Civil Engineers. Proceedings of the American Society of Civil Engineers Vol. 70, Issue 10
[page]

1944
*
American Society of Civil Engineers. Proceedings of the American Society of Civil Engineers
*

The author’s conclusions recommending that

*stability**be*secured by in- creasing weight and depth*must**be*rejected. ... In other words, the structure*whose*satisfactory static rigidity has been achieved the most economically will also*be*aerodynamically*stable*, or can*be*made so the most economically. ...
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