Positive invariance and asymptotic stability of solutions to certain Riccati equations

Hendrik J. Kuiper

doi:10.1080/02681119408806187

Positive invariance and asymptotic stability of solutions to certain Riccati equations

Hendrik J. Kuiper

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Matrix and operator Riccati equations of the form X'= −AX − XD + B + XCX with A and D positive definite arise in the study of transport processes. In this paper conditions are found that imply the unit ball ‖X‖≤1 is positively invariant. Also obtained are results on uniqueness, stability and asymptotic stability of steady states.

Original language	English (US)
Pages (from-to)	331-344
Number of pages	14
Journal	Dynamics and Stability of Systems
Volume	9
Issue number	4
DOIs	https://doi.org/10.1080/02681119408806187
State	Published - Jan 1 1994

ASJC Scopus subject areas

General Engineering

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10.1080/02681119408806187

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title = "Positive invariance and asymptotic stability of solutions to certain Riccati equations",

abstract = "Matrix and operator Riccati equations of the form X'= −AX − XD + B + XCX with A and D positive definite arise in the study of transport processes. In this paper conditions are found that imply the unit ball ‖X‖≤1 is positively invariant. Also obtained are results on uniqueness, stability and asymptotic stability of steady states.",

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AB - Matrix and operator Riccati equations of the form X'= −AX − XD + B + XCX with A and D positive definite arise in the study of transport processes. In this paper conditions are found that imply the unit ball ‖X‖≤1 is positively invariant. Also obtained are results on uniqueness, stability and asymptotic stability of steady states.

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Positive invariance and asymptotic stability of solutions to certain Riccati equations

Abstract

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