A comparison theorem for matrix Riccati difference equations

Harald K. Wimmer; Michele Pavon

doi:10.1016/0167-6911(92)90118-C

A comparison theorem for matrix Riccati difference equations

Harald K. Wimmer, Michele Pavon

Mathematics

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

Abstract

Difference equations of the form X(t) = F^*(t)X(t - 1)F(t) - F^*(t)X(t - 1)G(t)[I + G^*(t)X(t - 1)G(t)^-1G^*(t)X(t - 1)F(t) + Q(t) and their associated Hermitian matrices H(t) = (_F^{QF^*}_-GG^*)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to the discrete-time LQ optimal control problem is given.

Original language	English (US)
Pages (from-to)	233-239
Number of pages	7
Journal	Systems and Control Letters
Volume	19
Issue number	3
DOIs	https://doi.org/10.1016/0167-6911(92)90118-C
State	Published - Sep 1992

Keywords

discrete-time LQ optimal control
Matrix Riccati difference equations
monotonicity of solutions

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/0167-6911(92)90118-C

Cite this

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title = "A comparison theorem for matrix Riccati difference equations",

abstract = "Difference equations of the form X(t) = F*(t)X(t - 1)F(t) - F*(t)X(t - 1)G(t)[I + G*(t)X(t - 1)G(t)-1G*(t)X(t - 1)F(t) + Q(t) and their associated Hermitian matrices H(t) = (FQF*-GG *)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to the discrete-time LQ optimal control problem is given.",

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AU - Wimmer, Harald K.

AU - Pavon, Michele

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N2 - Difference equations of the form X(t) = F*(t)X(t - 1)F(t) - F*(t)X(t - 1)G(t)[I + G*(t)X(t - 1)G(t)-1G*(t)X(t - 1)F(t) + Q(t) and their associated Hermitian matrices H(t) = (FQF*-GG *)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to the discrete-time LQ optimal control problem is given.

AB - Difference equations of the form X(t) = F*(t)X(t - 1)F(t) - F*(t)X(t - 1)G(t)[I + G*(t)X(t - 1)G(t)-1G*(t)X(t - 1)F(t) + Q(t) and their associated Hermitian matrices H(t) = (FQF*-GG *)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to the discrete-time LQ optimal control problem is given.

KW - discrete-time LQ optimal control

KW - Matrix Riccati difference equations

KW - monotonicity of solutions

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JO - Systems and Control Letters

JF - Systems and Control Letters

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ER -

A comparison theorem for matrix Riccati difference equations

Abstract

Keywords

ASJC Scopus subject areas

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