Differential equations with positive evolutions and some applications
type: Item
instance of: scholarly article
title: Differential equations with positive evolutions and some applications
zbMATH Open document ID: 1117.34053
DOI: 10.1007/BF03323366
author: Tobias Damm
author: Toader Morozan
author: Vasile Dragan
author: Gerhard Freiling
published in: Results in Mathematics
publication date: 2007-01-23T00:00:00Z
review text: The authors present some basic properties of finite dimensional ordered vector spaces, introduce positive equations and provide some characterizations for their generators. The fourth section of the paper is concerned with exponential stability of positive solutions and to Lyapunov type theorems. After that, the authors obtain some characterizations for uniform observability and deduce a robustness theorem for positive evolutions with respect to positive perturbations of their generators. Finally, they apply their main results to the study of the qualitative properties of differential Riccati equations, arising in game theory.
reviewed by: Bogdan Sasu
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 91A99
zbMATH DE Number: 5117896
zbMATH Keywords: positive solution
zbMATH Keywords: generator
zbMATH Keywords: stability
MaRDI profile type: Publication
cites work: Matrix Riccati equations in control and systems theory
cites work: New Results in Linear System Stability
cites work: One-parameter semigroups of positive operators
cites work: Resolvent Positive Operators
cites work: Linear quadratic Nash games on positive linear systems
cites work: Q4317892
cites work: Q5594821
cites work: Q3996218
cites work: Q4326384
cites work: Rational matrix equations in stochastic control.
cites work: Newton's method for concave operators with resolvent positive derivatives in ordered Banach spaces
cites work: Q4816735
cites work: Stochastic observability and applications
cites work: Observability and detectability of a class of discrete-time stochastic linear systems
cites work: Quasimonotonie und Ungleichungen in halbgeordneten Räumen
cites work: Stability radii of Metzler operators
cites work: Properties of the solutions of rational matrix difference equations
cites work: Generalized Riccati difference and differential equations
cites work: Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices
cites work: Differential equations: Stability, oscillations, time lags
cites work: Q4329682
cites work: Positive 1D and 2D systems
cites work: Q4401802
cites work: Positive operators and an inertia theorem
cites work: Cross-Positive Matrices
description: scientific article; zbMATH DE number 5117896