Nonlinear coprime factorizations and parametrization of a class of stabilizing controllers

A simple approach to nonlinear state feedback design

“…Alternative approaches to the control of nonlinear systems can be found in [11], [12], [5], [6], [18], [3], [17], [7], [2], [14], [16], [19], [15], [8], [1], [4], [13] and [9], in the references cited in these publications, and elsewhere.…”

“…When the target domain D 0 is a tight neighborhood of the origin, these controllers yield asymptotic stabilization of Σ (section VI). 1 Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA hammer@mst.ufl.edu Explicitly, the controlled system is described by…”

“…As before, at each point x ∈ D 2 , choose a value u(x) ∈ U 2 (x) and define the state feedback function ϕ(x) := u(x). The set U 2 (x) and the domain D 2 are calculated by solving an inequality based on the function f given in (1). Then, the derivativė x(t) = f (x(t), ϕ(x(t))) points toward D 1 at all points x(t) of D 2 , and the state trajectory x(t) takes Σ ϕ from every point of D 2 toward D 1 .…”