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ON THE ASYMPTOTIC STABILITY OF LINEAR DISCRETE TIME DELAY SYSTEMS

S. B. STOJANOVIC, D. LJ. DEBELJKOVIC
2004 Advances in Dynamics, Instrumentation and Control  
Several sufficient conditions for asymptotic stability of linear discrete -delay systems were presented in the paper of Mori et al. (1982) .  ...  This paper extends some of the basic results in the area of Lyapunov (asymptotic) to linear, discrete, time invariant time-delay systems.  ...  Several sufficient conditions for asymptotic stability of linear discrete -delay systems were presented in the paper of Mori et al. (1982) .  ... 
doi:10.1142/9789812702289_0004 fatcat:4cyesxa5jrdcppjvrcxoezbcny

On the Global Asymptotic Stability of a Second-Order System of Difference Equations

Ibrahim Yalcinkaya
2008 Discrete Dynamics in Nature and Society  
A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations where the parameter and the initial values (for .  ...  Discrete Dynamics in Nature and Society Moreover, by virtue of Lemmas 2.2 ii and 2.5 resp., 2.6 , one can see that 3.2 holds. Therefore, the proof is complete.  ...  We must show that the positive equilibrium point x, y 1, 1 of the system 1.9 is both locally asymptotically stable and x n , y n → x, y as n → ∞ or equivalently Discrete Dynamics in Nature and Society  ... 
doi:10.1155/2008/860152 fatcat:27xazjikv5aehexbdstnh7hisq

On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation

Tetsu Mizumachi, Dmitry Pelinovsky
2012 Discrete and Continuous Dynamical Systems. Series S  
Asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation was earlier established for septic and higher-order nonlinear terms by using Strichartz estimate.  ...  The first author is supported by Grant-in-Aid for Scientific Research (No. 21540220). The second author is supported by the NSERC Discovery grant.  ...  Using the Strichartz estimate, asymptotic stability of localized modes with small |ω−ω 0 | was established in the DNLS equation (1.1) with p ≥ 3, that is, for septic and higher-order nonlinear terms [  ... 
doi:10.3934/dcdss.2012.5.971 fatcat:26ci2acmjzgujaot2c2qhxb67e

On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays

M. de la Sen, A. Ibeas
2008 Discrete Dynamics in Nature and Society  
It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent  ...  This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters.  ...  Asymptotic stability dependent on the delays Consider the nth order linear time-varying dynamic system with q internal in general, incommensurate known point delays: x t q j 0 A j t x t − h j 2.1 for any  ... 
doi:10.1155/2008/231710 fatcat:kud4twyy5vaihdhusv4a6uxlqa

Existence and Global Asymptotical Stability of Periodic Solution for theT-Periodic Logistic System with Time-Varying Generating Operators andT0-Periodic Impulsive Perturbations on Banach Spaces

JinRong Wang, X. Xiang, W. Wei, Qian Chen
2008 Discrete Dynamics in Nature and Society  
This paper studies the existence and global asymptotical stability of periodic PC-mild solution for theT-periodic Logistic system with time-varying generating operators andT0-periodic impulsive perturbations  ...  on Banach spaces.  ...  Especially, there are many results of periodic solutions such as existence and stability for impulsive periodic systems on finite dimensional spaces see 7-9 .  ... 
doi:10.1155/2008/524945 fatcat:ors5fmqcyjb3boyb4xheug4xym

On asymptotic stability of linear stochastic Volterra difference equations with respect to a fading perturbation

John A. D. Appleby, Markus Riedle, Alexandra Rodkina
Advances in Discrete Dynamical Systems   unpublished
The paper concerns studies the stochastic stability and stochastic asymptotic stability of the equilibrium solution of a nonlinear Volterra difference equation which is subject to stochastic state independent  ...  It is shown that if the linearized deterministic equation has summable solutions, then the nonlinear stochastic equation will be stable or asymptotically stable, provided that the initial condition, and  ...  The second author was partially supported by the Boole Centre for Research in Informatics, University College Cork, and by Mona Research Fellowship Programm awarded by the University of the West Indies  ... 
doi:10.2969/aspm/05310271 fatcat:mtbf2jamenawzamjca63tesjei

Perturbation of periodic orbits of Rabinovich system [article]

Anania Gîrban
2017 arXiv   pre-print
In this paper we stabilize asymptotically the periodic orbits of the Rabinovich system.  ...  In the paper [6] the Rabinovich system is modeled as a Hamilton-Poisson dynamical system on a Poisson manifold with one Casimir and consequently, the dynamics is given by common level set of the Casimir  ...  But, in the first two cases, we can't obtain the global asymptotic stability because the dynamics is located on the common level surfaces Hamilto-nian=constant or Casimir=constant and at least one of them  ... 
arXiv:1706.07293v1 fatcat:gfsjgqr2rvgajaa2j3dkc46oze

On the Stability and Control of Nonlinear Dynamical Systems via Vector Lyapunov Functions

S.G. Nersesov, W.M. Haddad
2006 IEEE Transactions on Automatic Control  
INTRODUCTION O NE OF THE MOST basic issues in system theory is the stability of dynamical systems.  ...  In addition, we introduce the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, and show that asymptotic stabilizability of a nonlinear dynamical system is  ...  on the state of a dynamical system.  ... 
doi:10.1109/tac.2005.863496 fatcat:foruoliqc5a3jngwe7usijeajm

A note on the problem of semiglobal practical stabilization of uncertain nonlinear systems via dynamic output feedback

A. Isidori, A.R. Teel, L. Praly
2000 Systems & control letters (Print)  
It is known that if a system can be (robustly) globally asymptotically stabilized by means of a feedback that is driven by functions that are uniformly completely observable (UCO), then this system can  ...  The class of systems which satisfy this hypothesis includes any stabilizable and detectable linear system and any relative degree one nonlinear system which is stabilizable by dynamic output feedback.  ...  It is well known that a nonlinear system having relative degree one can be robustly semiglobally stabilized via output feedback if its zero dynamics are globally asymptotically stable.  ... 
doi:10.1016/s0167-6911(99)00083-3 fatcat:5uofjbd2cvaytmm23ackbcydmu

Stability theory for hybrid dynamical systems

Hui Ye, A.N. Michel, Ling Hou
1998 IEEE Transactions on Automatic Control  
We then establish sufficient conditions for uniform stability, uniform asymptotic stability, exponential stability, and instability of an invariant set of hybrid dynamical systems.  ...  In addition to the above, we also establish sufficient conditions for the uniform boundedness of the motions of hybrid dynamical systems (Lagrange stability).  ...  For dynamical systems defined on abstract time space (i.e., for hybrid dynamical systems) we define various qualitative properties (such as Lyapunov stability, asymptotic stability, and so forth) in a  ... 
doi:10.1109/9.664149 fatcat:lco7cvfnl5csfkbkjguq6shokq

Global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weights

Youshen Xia, Jun Wang
2001 IEEE Transactions on Automatic Control  
In this case, the order of dynamic compensator which solves the DRPDC is given by E 3 := dim k2z z z Index Terms-Asymmetric connection weights, global asymptotic stability, neural networks.  ...  635 if and only if there exists a (C(1); A(1); B(1))-pair (V1(1); V2(1)) such that ImE V1(k) V2(k) KerD(k) for all k 2 Z Z Z: In this case, the minimal order of dynamic compensator which solves the DRPDC  ...  In this note, based on a new Lyapunov function, we investigate the global asymptotic stability of the dynamic neural system with asymmetric connection weights.  ... 
doi:10.1109/9.917666 fatcat:rbo3gjzo6bgeff66k5bmp6lgla

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.  ...  For this reason, on the way to the main result, it is shown that such dynamics are not necessarily Hamiltonian.  ...  In the first one, the problem of noninteraction with (simple) stability is solved by means of dynamic state feedback for a system having an unstable zero dynamics; in the second one, it is shown that the  ... 
doi:10.1016/s1474-6670(17)40368-5 fatcat:mbe3o3i5qnhgfptsocjxy42qim

A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon

Sanjay P. Bhat, Dennis S. Bernstein
2000 Systems & control letters (Print)  
We show that a continuous dynamical system on a state space that has the structure of a vector bundle on a compact manifold possesses no globally asymptotically stable equilibrium.  ...  In light of this result, we explain how attitude stabilizing controllers obtained using local coordinates lead to unwinding instead of global asymptotic stability.  ...  Strictly speaking, global asymptotic stability is not deÿned (in terms of attitude) for a controller that does not deÿne a dynamical system on the state space M.  ... 
doi:10.1016/s0167-6911(99)00090-0 fatcat:t4h5c7dhpva6nfxhwqxayl4oma

Stability of linear dynamic systems over the packet erasure channel: a co-design approach

Alireza Farhadi
2015 International Journal of Control  
This paper is concerned with the stability of linear time invariant dynamic systems over the packet erasure channel subject to minimum bit rate constraint when encoder and decoder are unaware of control  ...  time invariant dynamic systems over the packet erasure channel with feedback acknowledgment.  ...  In addition, one of the desired stability criteria for the stability of dynamic systems is almost sure stability criterion.  ... 
doi:10.1080/00207179.2015.1048292 fatcat:gowpo2vqaza6rjgr2mhaxmbawq

Stabilization of nonlinear systems via designed center manifold

Daizhan Cheng, C. Martin
2001 IEEE Transactions on Automatic Control  
It is proved that using this method, the first variables in each of the integral chains of the linearized part of the system do not affect the approximation order of the dynamics on the center manifold  ...  This paper addresses the problem of the local state feedback stabilization of a class of nonlinear systems with nonminimum phase zero dynamics.  ...  Now Theorem 2.4 assures the asymptotically stability of the dynamics on the center manifold and thus the stability of the closed-loop system.  ... 
doi:10.1109/9.948465 fatcat:j7l2pmun65hy7kqhffgtej2yay
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