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An Algebraic Problem in Control Theory

Published online by Cambridge University Press:  20 January 2009

Arthur Wouk
Arthur Wouk
Affiliation:
Mathematics Research Center, Madison, Wisconsin
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In the series of papers in the early forties summarised in (1), (2), A. I. Lur'e showed how to utilise Liapunov's second or direct method in the investigation of the stability of linear automatic control systems with a single nonlinear actuator. His approach consists of

1. the transformation of the original system of differential equations via the so-called Lur'e transformation into canonical coordinates in which the construction of the Liapunov function is direct, and

2. the conversion of the differential problem into a purely algebraic problem.

We will be concerned here with the questions of the existence and construction of the Lur's transformation.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 3 , June 1963 , pp. 205 - 218
Copyright
Copyright © Edinburgh Mathematical Society 1963

References

REFERENCES

(1) Lur'e, A. I., Some nonlinear problems in the theory of automatic control (Gos. Isdat. Tekh. Theor. Lit. Moscow, 1951; available in English from Her Majesty's Stationery Office, London (1957)).Google Scholar
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