A Simple Alternative to the Routh-Hurwitz Criterion for Symmetric Systems

1970 ◽  
Vol 37 (4) ◽  
pp. 1168-1170 ◽  
Author(s):  
T. J. Moran
Keyword(s):  
Asymptotic Stability ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Necessary And Sufficient Condition ◽  
Principal Coordinates ◽  
Simple Alternative ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Gyroscopic Systems ◽  
Symmetric Systems

A necessary and sufficient condition for the asymptotic stability of damped, linear, symmetric, multidegree of freedon systems is given. The condition is easily applied if the principal coordinates for the undamped system are known. The stability properties of such systems which are not asymptotically stable are investigated and the result is extended to gyroscopic systems.

Some Structural Properties of Systolic Tree Automata

1989 ◽  
Vol 12 (4) ◽  
pp. 571-585
Author(s):  
E. Fachini ◽  
A. Maggiolo Schettini ◽  
G. Resta ◽  
D. Sangiorgi
Keyword(s):  
Structural Properties ◽  
Stability Problem ◽  
Sufficient Condition ◽  
Tree Automata ◽  
Necessary And Sufficient Condition ◽  
The Stability ◽  
Necessary And Sufficient

We prove that the classes of languages accepted by systolic automata over t-ary trees (t-STA) are always either equal or incomparable if one varies t. We introduce systolic tree automata with base (T(b)-STA), a subclass of STA with interesting properties of modularity, and we give a necessary and sufficient condition for the equivalence between a T(b)-STA and a t-STA, for a given base b. Finally, we show that the stability problem for T(b)-ST A is decidible.

A Dynamic Duopoly Game with Content Providers’ Bounded Rationality

2020 ◽  
Vol 30 (07) ◽  
pp. 2050095 ◽  
Author(s):  
Hamid Garmani ◽  
Driss Ait Omar ◽  
Mohamed El Amrani ◽  
Mohamed Baslam ◽  
Mostafa Jourhmane
Keyword(s):  
Bounded Rationality ◽  
Chaotic Behavior ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Pricing Decisions ◽  
Dynamical Behaviors ◽  
Duopoly Model ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Dynamic Duopoly

This paper investigates the dynamical behaviors of a duopoly model with two content providers (CPs). Competition between two CPs is assumed to take place in terms of their pricing decisions and the credibility of content they offer. According to the CPs’ rationality level, we consider a scenario where both CPs are bounded rational. Each CP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamical system induced by bounded rationality, and establish a necessary and sufficient condition for stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control.

5.—The Uniform Asymptotic Stability of Certain Linear Differential-difference Equations

1976 ◽  
Vol 74 ◽  
pp. 71-79
Author(s):  
R. Datko
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Difference Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Asymptotic Stability ◽  
Linear Ordinary Differential Equations ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition is developed for determination of the uniform stability of a class of non-autonomous linear differential-difference equations. This condition is the analogue of the Liapunov criterion for linear ordinary differential equations.

scholarly journals Lyapunov-Krasovskii stability analysis of nonlinear integro-differential equation

2018 ◽  
Vol 7 (2) ◽  
pp. 53
Author(s):  
Prebo Jackreece
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Asymptotic Stability ◽  
Integro Differential Equation ◽  
Necessary And Sufficient

The purpose of this paper is to develop a qualitative stability analysis of a class of nonlinear integro-differential equation within the framework of Lyapunov-Krasovskii. We show that the existence of a Lyapunov-Krasovskii functional is a necessary and sufficient condition for the uniform asymptotic stability of the nonlinear Volterra integro-differential equations.

A New Algorithm for Testing the Stability of a Polytope: A Geometric Approach for Simplification

1996 ◽  
Vol 118 (3) ◽  
pp. 611-615 ◽  
Author(s):  
Jinsiang Shaw ◽  
Suhada Jayasuriya
Keyword(s):  
Characteristic Equation ◽  
Robust Stability ◽  
Geometric Structure ◽  
Geometric Approach ◽  
Geometric Interpretation ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Edge Theorem

Considered in this paper is the robust stability of a class of systems in which a relevant characteristic equation is a family of polynomials F: f(s, q) = a0(q) + a1(q)s + … + an(q)sn with its coefficients ai(q) depending linearly on q unknown-but-bounded parameters, q = (p1, p2, …, pq)T. It is known that a necessary and sufficient condition for determining the stability of such a family of polynomials is that polynomials at all the exposed edges of the polytope of F in the coefficient space be stable (the edge theorem of Bartlett et al., 1988). The geometric structure of such a family of polynomials is investigated and an approach is given, by which the number of edges of the polytope that need to be checked for stability can be reduced considerably. An example is included to illustrate the benefit of this geometric interpretation.

scholarly journals Stability Analysis ofθ-Methods for Neutral Multidelay Integrodifferential System

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Y. Xu ◽  
J. J. Zhao ◽  
Z. N. Sui
Keyword(s):  
Numerical Stability ◽  
Numerical Experiments ◽  
Analytic Solutions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Neutral Delay ◽  
Integrodifferential System ◽  
System A ◽  
The Stability ◽  
Necessary And Sufficient

This paper studies the stability of a class of neutral delay integrodifferential system. A necessary and sufficient condition of stability for its analytic solutions is considered. The improvedθ-methods are developed. Some numerical stability properties are obtained and numerical experiments are given.

On the stability of some solutions of the Stefan problem

1991 ◽  
Vol 2 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Riccardo Ricci ◽  
Xie Weiqing
Keyword(s):  
Stefan Problem ◽  
Travelling Wave ◽  
Sufficient Condition ◽  
Travelling Wave Solutions ◽  
Necessary And Sufficient Condition ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Necessary And Sufficient ◽  
Travelling Wave Front

We investigate the stability of travelling wave solutions of the one-dimensional under-cooled Stefan problem. We find a necessary and sufficient condition on the initial datum under which the free boundary is asymptotic to a travelling wave front. The method applies also to other types of solutions.

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