Abstract
This paper deals with the question of the existence of weak and strong common quadratic Lyapunov functions (CQLFs) for stable discrete-time linear timeinvariant (LTI) systems. The main result of the paper provides a simple characterisation of pairs of such systems for which a weak CQLF of a given form exists but for which no strong CQLF exists. An application of this result to second order discrete-time LTI systems is presented.
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