Asymptotic linearization of uncertain systems by variable structure control (Q1117180)

A nonlinear control system with uncertain dynamics described by a scalar differential inclusion of order n, \[ (1)\quad r^{(n)}\in G(t,r,\dot r,...,r^{(n-1)},u),\quad t\geq 0,\quad (2)\quad u\in U=[a,b], \] where the initial state x(0) is uncertain but bounded \[ (3)\quad | x(0)| \leq C \] is considered. Based on the knowledge of upper and lower estimates of the unknown dynamics, the authors show that the system (1)-(3) can be transformed to an asymptotically equivalent linear model \[ \dot y_ 1=y_ 2,...,\dot y_{n-1}=y_ n,\quad \dot y_ n=\sum^{n}_{i=1}a_ iy_ i+bv,\quad y(0)\quad fixed,\quad v\in V \] by using an (explicitly described) discontinuous feedback control law of variable structure type.