Contraction and related mappings: theory and applications

This paper discusses the theoretical aspects of contraction and related mappings and their application to certain systems engineering problems. It is demonstrated how the fixed point property of contraction mappings can be exploited to establish sufficient conditions for the stability of a class of nonlinear systems, as also to generate the actual output of the system to a given bounded input. Use of contraction and modified contraction methods for the iterative solution of sets of nonlinear algebraic equations is discussed. Numerical examples are given, and applications to Control and Power Systems problems cited and described