Nonlinearities enhance parameter convergence: the strict-feedback case

Following the development of a parameter convergence analysis procedure for output-feedback nonlinear systems, we shift our attention to strict-feedback nonlinear systems. We 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, we show that this convergence is exponential. Finally, we 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 null space of this matrix