Convex invertible cones of matrices - A unified framework for the equations of Sylvester, Lyapunov and Riccati

Izchak Lewkowicz

doi:10.1016/S0024-3795(98)10164-7

Convex invertible cones of matrices - A unified framework for the equations of Sylvester, Lyapunov and Riccati

Izchak Lewkowicz

School of Electrical and Computer Engineering

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

14 Scopus citations

Abstract

Convex cones of matrices which are closed under matrix inversion were defined and various connections with the algebraic Lyapunov equation of general inertia were studied in (N. Cohen, I. Lewkowicz, Linear Algebra and its Appl. 250 (1997) 105-131). Here, in the price of doubling the size of the matrices involved, we introduce a unified framework for the equations of Sylvester, Lyapunov and Riccati. This enables one to extend the convex invertible cone structure to all these three equations and explore related properties. In particular, the use of the Matrix Sign Function for solving these equations is examined.

Original language	English
Pages (from-to)	107-133
Number of pages	27
Journal	Linear Algebra and Its Applications
Volume	286
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(98)10164-7
State	Published - 1 Jan 1999

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/S0024-3795(98)10164-7

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abstract = "Convex cones of matrices which are closed under matrix inversion were defined and various connections with the algebraic Lyapunov equation of general inertia were studied in (N. Cohen, I. Lewkowicz, Linear Algebra and its Appl. 250 (1997) 105-131). Here, in the price of doubling the size of the matrices involved, we introduce a unified framework for the equations of Sylvester, Lyapunov and Riccati. This enables one to extend the convex invertible cone structure to all these three equations and explore related properties. In particular, the use of the Matrix Sign Function for solving these equations is examined.",

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Convex invertible cones of matrices - A unified framework for the equations of Sylvester, Lyapunov and Riccati

Abstract

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