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Finite time stability and comparison principles*

Published online by Cambridge University Press:  24 October 2008

A. A. Kayande  and
J. S. W. Wong
A. A. Kayande
Affiliation:
University of Alberta, Edmonton, Canada
J. S. W. Wong
Affiliation:
University of Alberta, Edmonton, Canada
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Extract

Motivated by discussion on practical stability in LaSalle and Lefschetz (3), Weiss and Infante (5), have discussed various notions of stability over finite time interval of a given differential system. This theory of stability differs from the usual stability theory mainly by the preassigned limits to which any given solution of the differential system must adhere. Sufficient conditions for these notions of stability are given in (5) in terms of certain Lyapunov-like functions satisfying some appropriate differential inequalities. The purpose of this article is to introduce some complementary notions of finite time stability and weaken the conditions on the differential inequalities involving Lyapunov-like functions by the use of comparison principles.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 749 - 756
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

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