A Classification of Nonlinear Systems Based on the Invariant Subdistribution Algorithm

Abstract

Consider a nonlinear system of the form

$$ \dot{x} = f(x) + \sum\limits_{{i = 1}}^m {{g_i}(x){u_i}} y = h(x) $$

(1.1)

with state x ∈ X Ì ℝⁿ, input u ∈ ℝ^m and output y ∈ ℝ^P; f and g₁,...,g_m are analytic vector fields on X and h is an analytic function.