Monotonicity and stabilizability- properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples

Robert R. Bitmead; Michel R. Gevers; Ian R. Petersen; R. John Kaye

doi:10.1016/0167-6911(85)90027-1

Monotonicity and stabilizability- properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples

Robert R. Bitmead^*
, Michel R. Gevers
, Ian R. Petersen
, R. John Kaye

^*Corresponding author for this work

The Australian National University

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

106 Citations (Scopus)

Abstract

The problem considered is that of selecting an initial covariance matrix for the Kalman filter to ensure that the closed-loop filter at every subsequent time instant is exponentially asymptotically stable as a time-invariant filter. Sufficient conditions are derived based on monotonicity properties of the solution of the Riccati difference equation. The results have application in observer design, and the cases of filtering for nonstabilizable systems and systems with singular system matrices are included.

Original language	English
Pages (from-to)	309-315
Number of pages	7
Journal	Systems and Control Letters
Volume	5
Issue number	5
DOIs	https://doi.org/10.1016/0167-6911(85)90027-1
Publication status	Published - Apr 1985

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10.1016/0167-6911(85)90027-1

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title = "Monotonicity and stabilizability- properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples",

abstract = "The problem considered is that of selecting an initial covariance matrix for the Kalman filter to ensure that the closed-loop filter at every subsequent time instant is exponentially asymptotically stable as a time-invariant filter. Sufficient conditions are derived based on monotonicity properties of the solution of the Riccati difference equation. The results have application in observer design, and the cases of filtering for nonstabilizable systems and systems with singular system matrices are included.",

keywords = "Kalman filtering, Riccati difference equation, Stabilizability",

author = "Bitmead, \{Robert R.\} and Gevers, \{Michel R.\} and Petersen, \{Ian R.\} and Kaye, \{R. John\}",

year = "1985",

month = apr,

doi = "10.1016/0167-6911(85)90027-1",

language = "English",

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Monotonicity and stabilizability- properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples. / Bitmead, Robert R.; Gevers, Michel R.; Petersen, Ian R. et al.
In: Systems and Control Letters, Vol. 5, No. 5, 04.1985, p. 309-315.

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

TY - JOUR

T1 - Monotonicity and stabilizability- properties of solutions of the Riccati difference equation

T2 - Propositions, lemmas, theorems, fallacious conjectures and counterexamples

AU - Bitmead, Robert R.

AU - Gevers, Michel R.

AU - Petersen, Ian R.

AU - Kaye, R. John

PY - 1985/4

Y1 - 1985/4

N2 - The problem considered is that of selecting an initial covariance matrix for the Kalman filter to ensure that the closed-loop filter at every subsequent time instant is exponentially asymptotically stable as a time-invariant filter. Sufficient conditions are derived based on monotonicity properties of the solution of the Riccati difference equation. The results have application in observer design, and the cases of filtering for nonstabilizable systems and systems with singular system matrices are included.

AB - The problem considered is that of selecting an initial covariance matrix for the Kalman filter to ensure that the closed-loop filter at every subsequent time instant is exponentially asymptotically stable as a time-invariant filter. Sufficient conditions are derived based on monotonicity properties of the solution of the Riccati difference equation. The results have application in observer design, and the cases of filtering for nonstabilizable systems and systems with singular system matrices are included.

KW - Kalman filtering

KW - Riccati difference equation

KW - Stabilizability

UR - https://www.scopus.com/pages/publications/0022043243

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DO - 10.1016/0167-6911(85)90027-1

M3 - Article

AN - SCOPUS:0022043243

SN - 0167-6911

VL - 5

SP - 309

EP - 315

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 5

ER -

Monotonicity and stabilizability- properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples

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