Design of controllers to solve the robust servomechanism problem for a class of nonlinear systems

This paper considers the following problem: given a nonlinear single-input, single-output system y = (c1 c2 c3...cn)x + f?? where ai=ai(??), i=1,2,...,n, ci=ci(??), i=1,2,...,n, b=b(??), where ??g\´x, it is desired to find a controller which solves the robust servomechanism problem for (I) so that robust asymptotic tracking occurs for all constant disturbances ?? and all constant set-points, and such that the resultant closed loop system is globally asymptotically stable. Sufficient conditions are obtained to solve this problem, and an algorithm for obtaining a suitable controller is given. The controller obtained is a type of "gain-scheduling" controller. An extension of the result is then made to multivariable systems, and an application is made to an n-link rigid robotic manipulator problem.