On the Input-Output Behavior of a Class of Second-Order Nonlinear Adaptive Systems

The paper deals with a class of second-order nonlinear nonautonomous systems which occur frequently in the context of adaptive control of linear plants with unknown parameters. In the absence of external inputs, such systems are (i) uniformly stable, and (ii) uniformly asymptotically stable when their nonautonomous components are persistently exciting. When external inputs are present, the stability behavior of these systems are critically dependent on the nature of these inputs. This paper presents sufficient conditions for the stability and instablity of the nonlinear system for different kinds of external input. These results have important implications on the design of robust adaptive systems.