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Uniform asymptotic stability of linear non-autonomous systems

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1 Author(s)

In this paper a new method is developed for obtaining necessary and sufficient conditions which, when satisfied, guarantee that a linear non-autonomous system will be uniformly asymptotically stable. The method is essentially an extension of two earlier theorems on the asymptotic stability of linear autonomous systems; these theorems, developed by the same author, are here extended to non-autonomous systems. Basically, the method consists of ascertaining whether a certain matrix is positive definite. In general, it is shown that this knowledge is necessary and sufficient to determine whether a linear non-autonomous system is exponentially stable and hence uniformly asymptotically stable.

Published in:

Canadian Journal of Electrical and Computer Engineering  (Volume:28 ,  Issue: 3/4 )