Hautus lemma information

In control theory and in particular when studying the properties of a linear time-invariant system in state space form, the Hautus lemma (after Malo L. J. Hautus), also commonly known as the Popov-Belevitch-Hautus test or PBH test,^[1]^[2] can prove to be a powerful tool.

A special case of this result appeared first in 1963 in a paper by Elmer G. Gilbert,^[1] and was later expanded to the current PHB test with contributions by Vasile M. Popov in 1966,^[3]^[4] Vitold Belevitch in 1968,^[5] and Malo Hautus in 1969,^[5] who emphasized its applicability in proving results for linear time-invariant systems.

^ ^a ^b Hespanha, Joao (2018). Linear Systems Theory (Second ed.). Princeton University Press. ISBN 9780691179575.
^ Bernstein, Dennis S. (2018). Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas (Revised and expanded ed.). Princeton University Press. ISBN 9780691151205.
^ Popov, Vasile Mihai (1966). Hiperstabilitatea sistemelor automate [Hyperstability of Control Systems]. Editura Academiei Republicii Socialiste România.
^ Popov, V.M. (1973). Hyperstability of Control Systems. Berlin: Springer-Verlag.
^ ^a ^b Belevitch, V. (1968). Classical Network Theory. San Francisco: Holden–Day.

[:0-1] Hespanha, Joao (2018). Linear Systems Theory (Second ed.). Princeton University Press. ISBN 9780691179575.

[2] Bernstein, Dennis S. (2018). Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas (Revised and expanded ed.). Princeton University Press. ISBN 9780691151205.

[3] Popov, Vasile Mihai (1966). Hiperstabilitatea sistemelor automate [Hyperstability of Control Systems]. Editura Academiei Republicii Socialiste România.

[4] Popov, V.M. (1973). Hyperstability of Control Systems. Berlin: Springer-Verlag.

[:1-5] Belevitch, V. (1968). Classical Network Theory. San Francisco: Holden–Day.

Hautus lemma information

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