Abstract
The second method of Liapunov has been extensively used to study the stability of discrete time systems on C? The theory has been surveyed by Kalman and Bertram [6], and many references are cited by Weiss [II]. M ore recently, converse theorems [12], some beginnings on structural stability [4], and finite time stability [Ill, have appeared. Two problems are central: (a) The difficulty of constructing suitable Liapunov functions, and (b) Estimation of the region of attraction for a nonglobal stable equilibrium. The stimulating articles of Willems [14] and Baker and Bergen [l] attack the first, whilst some progress has been made on the second in [IO, 131. These works considered continuous systems only. This note discusses the autonomous system
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