On Optimal Stabilization of Nonautonomous Systems

Abstract

Consider a controlled system of differential equations of perturbed motion

$$ \dot x = X(t,x;u), $$

(18.1)

where x = (x ₁,…, x _n), X = (X₁,…, X _n ), u = (u₁,…,u _r ). Suppose that functions X(t, x, u) are defined, continuous, and satisfying a Lipschitz condition in x in the domain

$$ t \in R, \left\| x \right\| < H (H = const). $$

(18.2)