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.

ROBUST STABILITY OF MULTI-DIMENSIONAL (m-D) DISCRETE INTERVAL SYSTEMS AND APPLICATIONS

1991 ◽  
Vol 01 (01) ◽  
pp. 93-104 ◽  
Author(s):  
P. BAUER
Keyword(s):  
Robust Stability ◽  
Discrete Systems ◽  
Sufficient Condition ◽  
Invariant System ◽  
Necessary And Sufficient Condition ◽  
Interval System ◽  
Discrete Interval ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Interval Systems

Robust stability of m-D discrete systems, represented by a m-D difference equation is analyzed. A sufficient condition for stability is derived, which requires the stability of one linear shift-invariant system. For special classes of systems, the stability of one corner of the interval system is a necessary and sufficient condition. The results are applicable to shift-variant and shift-invariant interval m-D systems. Applications and illustrative examples are also provided.

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.

scholarly journals Isometric Signal Processing under Information Geometric Framework

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 332 ◽  
Author(s):  
Hao Wu ◽  
Yongqiang Cheng ◽  
Hongqiang Wang
Keyword(s):  
Signal Processing ◽  
Probability Distribution ◽  
Geometric Structure ◽  
Information Geometry ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Statistical Manifold ◽  
Intrinsic Parameter ◽  
Geometric Framework ◽  
Necessary And Sufficient

Information geometry is the study of the intrinsic geometric properties of manifolds consisting of a probability distribution and provides a deeper understanding of statistical inference. Based on this discipline, this letter reports on the influence of the signal processing on the geometric structure of the statistical manifold in terms of estimation issues. This letter defines the intrinsic parameter submanifold, which reflects the essential geometric characteristics of the estimation issues. Moreover, the intrinsic parameter submanifold is proven to be a tighter one after signal processing. In addition, the necessary and sufficient condition of invariant signal processing of the geometric structure, i.e., isometric signal processing, is given. Specifically, considering the processing with the linear form, the construction method of linear isometric signal processing is proposed, and its properties are presented in this letter.

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.

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.

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