Stabilization of nonlinear systems by qualitative feedback controllers

Abstract

The paper considers the problem of stabilizing a non-linear plant by means of a qualitative controller [u(k)] = k([ x ( k)]) that has access only to the qualitative value [ x (k)] of the system state x(k) and can only determine one of a set of qualitative values [ u (k)] of the command input u ( k) Necessary and sufficient conditions for the existence of a stabilizing qualitative controller and a procedure for determining such a controller are given. These conditions and the design algorithm refer merely to a qualitative model of the system rather than the precise state-space description. The results are illustrated by a numerical example.