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On the elliptic ball stability criterion for ordinary differential equations

Published online by Cambridge University Press:  24 October 2008

Russell A. Smith
Russell A. Smith
Affiliation:
University of Durham
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Abstract

It is proved that the elliptic ball criterion is a necessary condition on the matrix M(t) for the linear feedback control equation f(D)x + BM(t)g(D)x = 0 to have a special kind of quadratic Lyapunov function. That it is also a sufficient condition has already been proved elsewhere. These two facts lead to a comparison theorem which enables the existence of a quadratic Lyapunov function for one equation to be deduced from that for another equation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 497 - 505
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

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