Stabilization by output continuous and pulse-modulated uncertain systems

Abstract

The system x˙ i = 'i(·) + xi+2, i ∈ 1, n − 2, x˙n−1 = 'n−1(·) + u1, x˙n = 'n(·) + u2, where 'i(·) are nonanticipating functionals of arbitrary nature with following properties |'i(·)| ≤ c Pi k=1 |xk(t)|, i ∈ 1, n, c = const, and u1 and u2 are stabilization, is considered. It is supposed that only outputs x1 and x2 are measurable. The problem of both continuous and impulsive stabilizations such u1, and u2 that make the system globally asymptotically stable is considered. The solution of this problem is based on constructing observed-based equations and quadratic Lyapunov function, and averaging method. Refs 9.