×

Bounds in algebraic Riccati and Lyapunov equations: A survey and some new results. (English) Zbl 0852.93005

Almost 200 bounds on algebraic Riccati and Lyapunov equations solutions are given, some of them new ones. Both continuous and discrete-time cases are considered. The bounds are for the eigenvalues, trace, determinant, norm. Among the references are also Trans. Soc. Intrum. Contr. Engineers in Japanese.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93B60 Eigenvalue problems
93B15 Realizations from input-output data
49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1109/TAC.1980.1102438 · Zbl 0469.93060
[2] DOI: 10.1080/00207178608933475 · Zbl 0591.15010
[3] DOI: 10.1109/TAC.1979.1102053 · Zbl 0404.93019
[4] DOI: 10.1080/00207729008910455 · Zbl 0707.93066
[5] DOI: 10.1109/TAC.1981.1102803 · Zbl 0501.93023
[6] DOI: 10.1109/TAC.1982.1102947
[7] DOI: 10.1109/TAC.1983.1103123 · Zbl 0507.15014
[8] DOI: 10.1109/9.151107
[9] DOI: 10.1109/9.250481 · Zbl 0775.93100
[10] DOI: 10.1109/9.377 · Zbl 0637.15009
[11] DOI: 10.1109/9.148377 · Zbl 0767.93043
[12] DOI: 10.1109/9.186326 · Zbl 0773.93053
[13] DOI: 10.1109/TAC.1977.1101441 · Zbl 0346.93029
[14] DOI: 10.1109/TAC.1986.1104327
[15] DOI: 10.1109/TAC.1985.1103858 · Zbl 0576.15009
[16] MIDDLETON R. H., Digitial Control and Estimation a Unified Approach (1990)
[17] DOI: 10.1109/TAC.1975.1101086 · Zbl 0317.93048
[18] MORI T., Transactions of the Society of Instrumentation and Control Engineers 62 pp 760– (1979)
[19] DOI: 10.1080/00207178408933163 · Zbl 0527.93030
[20] MORI T., Transactions of the Society of Instrumentation and Control Engineers 15 pp 986– (1979)
[21] MORI T., Transactions of the Society of Instrumentation and Electrical Engineers, Japan 100 pp 402– (1980)
[22] DOI: 10.1016/0167-6911(92)90109-6 · Zbl 0743.93075
[23] DOI: 10.1109/TAC.1978.1101676 · Zbl 0375.15009
[24] DOI: 10.1016/0167-6911(92)90084-6 · Zbl 0784.93075
[25] DOI: 10.1109/TAC.1974.1100682 · Zbl 0291.93035
[26] DOI: 10.1109/TAES.1978.308556
[27] DOI: 10.1080/00207178408933169 · Zbl 0542.15004
[28] DOI: 10.1109/TAC.1987.1104699 · Zbl 0617.15013
[29] DOI: 10.1109/TAC.1986.1104370 · Zbl 0616.15013
[30] DOI: 10.1109/TAC.1979.1102075 · Zbl 0409.93036
[31] DOI: 10.1049/el:19830097
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.