Abstract
In this chapter we consider practical stability of discrete systems on the basis of maximum sets of initial conditions concept. We propose results concerning nonlinear discrete systems including topological properties of the maximum sets of initial conditions for internal practical stability, the necessary and sufficient conditions of internal practical stability using the optimal Lyapunov function. Further we offer the analytical forms (such as the Minkowski function, the inverse Minkowski function, and the support function) of the maximum sets of initial conditions representation in linear case, optimal ellipsoidal estimations of practical stability domains, and optimal estimations of phase constraints. In the last section we consider the problem of external practical stability of discrete systems.
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