scholarly journals Stability conditions for some distributed systems: buffered random access systems

1994 ◽  
Vol 26 (2) ◽  
pp. 498-515 ◽  
Author(s):  
Wojciech Szpankowski
Keyword(s):  
Stability Region ◽  
Sufficient Conditions ◽  
Random Access ◽  
Symmetric System ◽  
Slotted Aloha ◽  
Stability Regions ◽  
Novel Technique ◽  
Token Passing ◽  
The Stability ◽  
Necessary And Sufficient

We consider the standard slotted ALOHA system with a finite number of buffered users. Stability analysis of such a system was initiated by Tsybakov and Mikhailov (1979). Since then several bounds on the stability region have been established; however, the exact stability region is known only for the symmetric system and two-user ALOHA. This paper proves necessary and sufficient conditions for stability of the ALOHA system. We accomplish this by means of a novel technique based on three simple observations: applying mathematical induction to a smaller copy of the system, isolating a single queue for which Loynes' stability criteria is adopted, and finally using stochastic dominance to verify the required stationarity assumptions in the Loynes criterion. We also point out that our technique can be used to assess stability regions for other multidimensional systems. We illustrate it by deriving stability regions for buffered systems with conflict resolution algorithms (see also Georgiadis and Szpankowski (1992) for similar approach applied to stability of token-passing rings).

scholarly journals Stability conditions for some distributed systems: buffered random access systems

1994 ◽  
Vol 26 (02) ◽  
pp. 498-515 ◽  
Author(s):  
Wojciech Szpankowski
Keyword(s):  
Stability Region ◽  
Sufficient Conditions ◽  
Random Access ◽  
Symmetric System ◽  
Slotted Aloha ◽  
Stability Regions ◽  
Novel Technique ◽  
Token Passing ◽  
The Stability ◽  
Necessary And Sufficient

We consider the standard slotted ALOHA system with a finite number of buffered users. Stability analysis of such a system was initiated by Tsybakov and Mikhailov (1979). Since then several bounds on the stability region have been established; however, the exact stability region is known only for the symmetric system and two-user ALOHA. This paper proves necessary and sufficient conditions for stability of the ALOHA system. We accomplish this by means of a novel technique based on three simple observations: applying mathematical induction to a smaller copy of the system, isolating a single queue for which Loynes' stability criteria is adopted, and finally using stochastic dominance to verify the required stationarity assumptions in the Loynes criterion. We also point out that our technique can be used to assess stability regions for other multidimensional systems. We illustrate it by deriving stability regions for buffered systems with conflict resolution algorithms (see also Georgiadis and Szpankowski (1992) for similar approach applied to stability of token-passing rings).

On the Stability of Linear Stochastic Differential Equations

1973 ◽  
Vol 40 (1) ◽  
pp. 87-92 ◽  
Author(s):  
F. Kozin ◽  
C.-M. Wu
Keyword(s):  
White Noise ◽  
Stability Region ◽  
Sufficient Conditions ◽  
Stability Conditions ◽  
Density Functions ◽  
Close Approximation ◽  
Sample Stability ◽  
Gaussian Coefficient ◽  
The Stability ◽  
Necessary And Sufficient

In this paper we present a study of the almost-sure sample stability properties of second-order linear systems with stochastic coefficients. Using knowledge of the first density functions of the coefficient processes, stability conditions are obtained. Based upon recent necessary and sufficient conditions for white-noise coefficient systems, the conditions obtained may yield a close approximation of the exact stability region for the Gaussian coefficient case.

Dynamics of Asymmetric Nonconservative Systems

1983 ◽  
Vol 50 (1) ◽  
pp. 199-203 ◽  
Author(s):  
D. J. Inman
Keyword(s):  
Sufficient Conditions ◽  
Symmetric System ◽  
Qualitative Behavior ◽  
Parameter System ◽  
Nonconservative Systems ◽  
Asymmetric System ◽  
Lumped Parameter ◽  
Stability And Instability ◽  
The Stability ◽  
Necessary And Sufficient

This work examines a linear, asymmetric lumped parameter system. Results on the qualitative behavior of a certain subclass of such systems are presented. In particular, necessary and sufficient conditions for the existence of a linear transformation that transforms an asymmetric system into an equivalent symmetric system are derived. Results on the stability and instability of such systems are presented and stated in terms of the original asymmetric system’s coefficient matrices. This work is compared with that of other authors and numerical examples illustrating the utility and correctness of the results are presented.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

Quasi-Periodic Motion and Hopf Bifurcation of a Two-Dimensional Aeroelastic Airfoil System in Supersonic Flow

2021 ◽  
Vol 31 (02) ◽  
pp. 2150018
Author(s):  
Wentao Huang ◽  
Chengcheng Cao ◽  
Dongping He
Keyword(s):  
Hopf Bifurcation ◽  
Sufficient Conditions ◽  
Theoretical Method ◽  
Simulation Method ◽  
Runge Kutta Method ◽  
Complex Roots ◽  
The Stability ◽  
Necessary And Sufficient ◽  
2D And 3D ◽  
Imaginary Roots

In this article, the complex dynamic behavior of a nonlinear aeroelastic airfoil model with cubic nonlinear pitching stiffness is investigated by applying a theoretical method and numerical simulation method. First, through calculating the Jacobian of the nonlinear system at equilibrium, we obtain necessary and sufficient conditions when this system has two classes of degenerated equilibria. They are described as: (1) one pair of purely imaginary roots and one pair of conjugate complex roots with negative real parts; (2) two pairs of purely imaginary roots under nonresonant conditions. Then, with the aid of center manifold and normal form theories, we not only derive the stability conditions of the initial and nonzero equilibria, but also get the explicit expressions of the critical bifurcation lines resulting in static bifurcation and Hopf bifurcation. Specifically, quasi-periodic motions on 2D and 3D tori are found in the neighborhoods of the initial and nonzero equilibria under certain parameter conditions. Finally, the numerical simulations performed by the fourth-order Runge–Kutta method provide a good agreement with the results of theoretical analysis.

Coupled Stability of Multiport Systems—Theory and Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 419-428 ◽  
Author(s):  
J. E. Colgate
Keyword(s):  
Stability Property ◽  
Force Feedback ◽  
Linear Time ◽  
Experimental Studies ◽  
Sufficient Conditions ◽  
Direct Drive ◽  
Property A ◽  
Linear Time Invariant ◽  
The Stability ◽  
Necessary And Sufficient

This paper presents both theoretical and experimental studies of the stability of dynamic interaction between a feedback controlled manipulator and a passive environment. Necessary and sufficient conditions for “coupled stability”—the stability of a linear, time-invariant n-port (e.g., a robot, linearized about an operating point) coupled to a passive, but otherwise arbitrary, environment—are presented. The problem of assessing coupled stability for a physical system (continuous time) with a discrete time controller is then addressed. It is demonstrated that such a system may exhibit the coupled stability property; however, analytical, or even inexpensive numerical conditions are difficult to obtain. Therefore, an approximate condition, based on easily computed multivariable Nyquist plots, is developed. This condition is used to analyze two controllers implemented on a two-link, direct drive robot. An impedance controller demonstrates that a feedback controlled manipulator may satisfy the coupled stability property. A LQG/LTR controller illustrates specific consequences of failure to meet the coupled stability criterion; it also illustrates how coupled instability may arise in the absence of force feedback. Two experimental procedures—measurement of endpoint admittance and interaction with springs and masses—are introduced and used to evaluate the above controllers. Theoretical and experimental results are compared.

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

scholarly journals Multiresolution analysis and wavelets on Vilenkin groups

2008 ◽  
Vol 21 (3) ◽  
pp. 309-325 ◽  
Author(s):  
Yury Farkov
Keyword(s):  
Multiresolution Analysis ◽  
Linear Independence ◽  
Sufficient Conditions ◽  
Partition Of Unity ◽  
Necessary And Sufficient Conditions ◽  
Refinable Functions ◽  
Vilenkin Groups ◽  
Orthogonal Wavelets ◽  
The Stability ◽  
Necessary And Sufficient

This paper gives a review of multiresolution analysis and compactly sup- ported orthogonal wavelets on Vilenkin groups. The Strang-Fix condition, the partition of unity property, the linear independence, the stability, and the orthonormality of 'integer shifts' of the corresponding refinable functions are considered. Necessary and sufficient conditions are given for refinable functions to generate a multiresolution analysis in the L2-spaces on Vilenkin groups. Several examples are provided to illustrate these results. .

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