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

John Foy
2004 Theoretical Computer Science  
to the correctness of ZF set theory-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.  ... 
doi:10.1016/j.tcs.2004.05.001 fatcat:nf4awspykvdkbp3fwz7kmzzgpy

A sufficient condition for stability of a polytope of matrices

Yuguang Fang, Kenneth A. Loparo, Xiangbo Feng
1994 Systems & control letters (Print)  
The results developed can also 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  ... 
doi:10.1016/0167-6911(94)90045-0 fatcat:poqp7naonfecpms6hvs5eguk6i

Stability of Real Parametric Polynomial Discrete Dynamical Systems

Fermin Franco-Medrano, Francisco J. Solis
2015 Discrete Dynamics in Nature and Society  
The exact boundary values of these 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.  ... 
doi:10.1155/2015/680970 fatcat:wjpktuxpbvha3nu4snjwpreox4

Codimension one generic homoclinic classes with interior

Rafael Potrie, Martin Sambarino
2010 Bulletin of the Brazilian Mathematical Society  
We study generic diffeomorphisms 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.  ... 
doi:10.1007/s00574-010-0006-z fatcat:7qexfa5awna6fddmgdckndd5nu

Output-input stability and minimum-phase nonlinear systems

D. Liberzon, A.S. Morse, E.D. Sontag
2002 IEEE Transactions on Automatic Control  
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  ...  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  ... 
doi:10.1109/9.989070 fatcat:luwuhhdyijbw7essxiwerlihie

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.  ... 

Complexity of Ten Decision Problems in Continuous Time Dynamical Systems [article]

Amir Ali Ahmadi, Anirudha Majumdar, Russ Tedrake
2012 arXiv   pre-print
of 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.  ... 
arXiv:1210.7420v1 fatcat:25m44ydiobdqdlxzn3c7qarlty

Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm

Chunjiang Qian, Wei Lin
2002 IEEE Transactions on Automatic Control  
For example, for 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.  ... 
doi:10.1109/tac.2002.803542 fatcat:nraxgqh5qvc2hn23lymernj2ru

Noninteracting Control with Stability for Hamiltonian Systems

A. Astolfi, L. Menini
1998 IFAC Proceedings Volumes  
The problem of noninteraction with 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.  ... 
doi:10.1016/s1474-6670(17)40368-5 fatcat:mbe3o3i5qnhgfptsocjxy42qim

State feedback impulsive therapy to SIS model of animal infectious diseases

Qiong Liu, Meng Zhang, Lansun Chen
2019 Physica A: Statistical Mechanics and its Applications  
Basing on the impulsive model, the existence of order-1 periodic solution and its 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).  ... 
doi:10.1016/j.physa.2018.09.161 pmid:32288107 pmcid:PMC7126221 fatcat:d53a6xan6vef7nialzepwu7wqm

Synchronization in On-Off Stochastic Networks: Windows of Opportunity

Russell Jeter, Igor Belykh
2015 IEEE Transactions on Circuits and Systems Part 1: Regular Papers  
We apply 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.  ... 
doi:10.1109/tcsi.2015.2415172 fatcat:7re2753gafg6vantkbqi2khhte

Instability, Modus ponens and uncertainty of deduction

Huajie Liu
2006 Frontiers of Philosophy in China  
Some kind of 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.  ... 
doi:10.1007/s11466-006-0030-7 fatcat:565f4fiwenasncavwvydchpfim

Generalized proportional-plus-derivative compensators for a class ofuncertain plants

SURESH M. JOSHI
1991 Journal of Guidance Control and Dynamics  
For the present problem, to 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.  ... 
doi:10.2514/3.20693 fatcat:r5uawmzwpvdcblu2fhfjhlos6e

Stability regions of nonlinear autonomous dynamical systems

H.-D. Chiang, M.W. Hirsch, F.F. Wu
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  ... 
doi:10.1109/9.357 fatcat:bai65jiuufhwhbr2atp5fm3i4y

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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