Linear Differential Equations with Positive Evolution on Ordered Banach Spaces

Vasile Dragan, Toader Morozan and Adrian-Mihail Stoica
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Vasile Dragan: Institute of Mathematics of the Romanian Academy
Toader Morozan: Institute of Mathematics of the Romanian Academy
Adrian-Mihail Stoica: University Politechnica of Bucharest

Chapter Chapter 2 in Mathematical Methods in Robust Control of Linear Stochastic Systems, 2013, pp 39-120 from Springer

Abstract: Abstract In this chapter the problem of exponential stability of the zero state equilibrium of a class of linear differential equations on a real ordered Banach space is investigated. The linear differential equations under consideration named differential equations with positive evolution are defined by a special class of strongly continuous operator valued functions. These differential equations are natural extensions to the time-varying case of linear differential equations with constant coefficients on an ordered Banach space defined by a linear and bounded operator with positive semigroup.

Keywords: Real Ordered Banach Space; Linear Differential Equations; Positive Development; Exponential Stability; Time-varying Case (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-8663-3_2

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DOI: 10.1007/978-1-4614-8663-3_2

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