Abstract
AbstractRecently, sufficient conditions for a time‐delay time‐varying (TDTV) system have been shown to be nonexpansive or bounded real (BR). Using this result, the sufficient conditions for stability of learning control for the TDTV system have been derived [2]. the characteristic of these sufficient conditions is independent of delay.This paper considers the relation between these obtained conditions and the similarity transformation of a TDTV system, and derives new sufficient conditions of the nonexpansive TDTV system which are invariant under block similarity transformation. New stability conditions also are derived for the learning control of the TDTV system. the new sufficient conditions include the parameter of delay length explicitly, and ensure that when the given TDTV system satisfies the new conditions, every TDTV system which is similar to the given systems is nonexpansive. It also is shown that under a certain condition, the new sufficient conditions guarantee the nonexpansivity of TDTV system even when the value of the time‐delay length of a real TDTV system deviates from the values in the sufficient condition. Finally, numerical examples are given to show that the obtained stability conditions of learning control are valid.
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