Nonlinearities enhance parameter convergence in strict feedback systems

Abstract

Following the development of a parameter convergence analysis procedure for output-feedback nonlinear systems (1995, 1998), the authors shift their attention to strict feedback nonlinear systems in this paper. They develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signal, to determine a priori whether or not the parameter estimates will converge to their true values, simply by checking the linear independence of the rows of a constant real matrix. Moreover, the authors show that this convergence is exponential. Finally, they prove that even if the rows of this constant matrix are not linearly independent, partial parameter convergence is still achieved, in the sense that the parameter error vector converges asymptotically to the left nullspace of this matrix.