Anderson, B. D.Moore, J. B.2026-01-022026-01-020013-5194ORCID:/0000-0002-1493-4774/work/174739938https://hdl.handle.net/1885/733803113The lemma of Lyapunov gives the necessary and sufficient condition for the stability of a time-invariant system in terms of the existence of a positive-definite symmetric matrix. In this letter, the lemma is generalised for time-varying systems, in which it is shown that additional conditions are required for the lemma to hold. The conditions involve boundedness of certain quantities and uniform complete observability of a pair of matrixes.2en196710.1049/el:196702253342967587