Fixed-point Theorems for Stability Analysis of Adaptive Systems

Abstract The use of fixed point theorems is considered for the stability analysis of adaptive systems. The particular fixed point theorems considered are the Contraction Mapping Principle of Banach and the Schauder Fixed Point Theorem. It is shown how the contraction property can be achieved by exponential stability of the homogeneous part of the linearized adaptive system. The region of linearization validity is estimated by considering fixed as well as adapti ve tuned systems. Fixed-point theorems are shown also to be useful for a transient analysis of the adaptive system.