Abstract

In this paper, we introduce two new types of local instabilities which exclusively pertain to a linear time-varying (LTV) system. Investigation of these local instabilities has lead to new necessary and sufficient conditions for a LTV system to be globally stable. It is shown that a direct extension of the stability conditions of a linear time-invariant (LTI) system is not applicable to a LTV system. The admissible area for a set of coefficients of a globally stable LTV system has been established and this area is found to be much larger than its LTI system counterpart.

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