Global asymptotic stability in discrete systems

AbstractSeveral types of discrete physical systems are characterized by difference equations. An often used mathematical model of discrete systems is that of a continuous mapping function T: Rn → Rn, where xi + 1 = T(xi), i = 0, 1, …. In the analysis and design of discrete systems, global asymptotic stability is an important consideration. For some related discussion see J. P. La Salle [1, pp. 20, 21].In this paper two theorems on global asymptotic stability are proven. The first theorem given below supplies the answer to the unknown system stability mentioned in [2, p. 188]. The special case of the theorem, where T′(x) is a linear transformation has been proved in [3]