Evenly Convex Polyhedra: Finite Linear Systems Containing Strict Inequalities

2020 ◽  
pp. 61-99
Author(s):  
María D. Fajardo ◽  
Miguel A. Goberna ◽  
Margarita M. L. Rodríguez ◽  
José Vicente-Pérez
Keyword(s):  
Linear Systems ◽  
Convex Polyhedra ◽  
Strict Inequalities ◽  
Finite Linear

scholarly journals On Finite Linear Systems Containing Strict Inequalities

2017 ◽  
Vol 173 (1) ◽  
pp. 131-154
Author(s):  
Margarita M. L. Rodríguez ◽  
José Vicente-Pérez
Keyword(s):  
Linear Systems ◽  
Strict Inequalities ◽  
Finite Linear

scholarly journals Simple and weak delta-invariant psolyhedral sets for discrete-time singular systems

2003 ◽  
Vol 14 (4) ◽  
pp. 339-347 ◽  
Author(s):  
Eugênio B. Castelan ◽  
Sophie Tarbouriech
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Initial Conditions ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Convex Polyhedra ◽  
Equivalent System ◽  
Positive Invariance ◽  
Regular Linear Systems ◽  
Necessary And Sufficient

In this paper, necessary and sufficient conditions for the positive invariance of convex polyhedra with respect to linear discrete-time singular systems subject to bounded additive disturbances are established. New notions of delta-invariance under different assumptions on the initial conditions are defined. Specifically, the notions of simple and weak delta-invariance are considered. They can be seen as extensions of the delta-positive invariance concept used for the regular linear systems with additive disturbances. The results are presented by considering classical equivalent system representations for linear singular systems.

scholarly journals On linear systems containing strict inequalities

2003 ◽  
Vol 360 ◽  
pp. 151-171 ◽  
Author(s):  
Miguel A. Goberna ◽  
Valentín Jornet ◽  
Margarita M.L. Rodríguez
Keyword(s):  
Linear Systems ◽  
Strict Inequalities

scholarly journals Analyzing linear systems containing strict inequalities via evenly convex hulls

2006 ◽  
Vol 169 (3) ◽  
pp. 1079-1095 ◽  
Author(s):  
Miguel A. Goberna ◽  
Margarita M.L. Rodrı́guez
Keyword(s):  
Linear Systems ◽  
Convex Hulls ◽  
Strict Inequalities

Evenly Convex Sets: Linear Systems Containing Strict Inequalities

2020 ◽  
pp. 1-60
Author(s):  
María D. Fajardo ◽  
Miguel A. Goberna ◽  
Margarita M. L. Rodríguez ◽  
José Vicente-Pérez
Keyword(s):  
Linear Systems ◽  
Convex Sets ◽  
Strict Inequalities

scholarly journals Computing the Cycle Structure of Finite Linear Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 4316-4321
Author(s):  
Eva Zerz ◽  
Hermann Giese
Keyword(s):  
Linear Systems ◽  
Cycle Structure ◽  
Finite Linear

scholarly journals Signal approximations by shifted Gaussians: a direct approach by finite linear systems

2020 ◽  
Vol 1479 ◽  
pp. 012046
Author(s):  
Sergei M Sitnik ◽  
Alexandr S Timashov ◽  
Sergei N Ushakov
Keyword(s):  
Linear Systems ◽  
Direct Approach ◽  
Finite Linear

Reserve of characteristic inclusion for interval linear systems of relations

2021 ◽  
pp. 61-85
Author(s):  
Ирина Александровна Шарая ◽  
Сергей Петрович Шарый
Keyword(s):  
Linear Systems ◽  
Interval Arithmetic ◽  
Quantitative Measure ◽  
Solution Set ◽  
Special Cases ◽  
Interval Linear ◽  
Strict Inequalities ◽  
Interval Linear Systems ◽  
Interval Systems ◽  
Linear Systems Of Equations

В работе рассматриваются интервальные линейные включения Cx ⊆ d в полной интервальной арифметике Каухера. Вводится количественная мера выполнения этого включения, названная “резервом включения”, исследуются ее свойства и приложения. Показано, что резерв включения оказывается полезным инструментом при изучении АЕ-решений и кванторных решений интервальных линейных систем уравнений и неравенств. В частности, использование резерва включения помогает при определении положения точки относительно множества решений, при исследовании пустоты множества решений или его внутренности и т.п In this paper, we consider interval linear inclusions Cx ⊆ d in the Kaucher complete interval arithmetic. These inclusions are important both on their own and because they provide equivalent and useful descriptions for the so-called quantifier solutions and AE-solutions to interval systems of linear algebraic relations of the form Ax σ b , where A is an interval m × n -matrix, x ∈ R , b is an interval m -vector, and σ ∈ {= , ≤ , ≥} . In other words, these are interval systems in which equations and non-strict inequalities can be mixed. Considering the inclusion Cx ⊆ d in the Kaucher complete interval arithmetic allows studing simultaneously and in a uniform way all the different special cases of quantifier solutions and AE-solutions of interval systems of linear relations, as well as using interval analysis methods. A quantitative measure, called the “inclusion reserve”, is introduced to characterize how strong the inclusion Cx ⊆ d is fulfilled. In our work, we investigate its properties and applications. It is shown that the inclusion reserve turns out to be a useful tool in the study of AE-solutions and quantifier solutions of interval linear systems of equations and inequalities. In particular, the use of the inclusion reserve helps to determine the position of a point relative to a solution set, in investigating whether the solution set is empty or not, whether a point is in the interior of the solution set, etc

Well-Posed Linear Systems

2005 ◽  
Author(s):  
Olof Staffans
Keyword(s):  
Linear Systems ◽  
Well Posed
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