Asymptotic stabilization of a system of coupled $${\varvec{n}}$$th-order differential equations with potentially unbounded high-frequency oscillating perturbations

Abstract

This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled nth-order ordinary differential equations in the presence of a nonvanishing at x = 0 or even unbounded on the time interval [0, ∞) timevarying high-frequency oscillating perturbation w(t, x). The obtained results generalize and extend some known and now classical results in the control theory for a wider class of perturbations. Moreover, as is shown in the paper, there is no room for further generalization for w which is time-dependent only, w = w(t).

When Is σ (A(t)) ⊂ {z ∈ ℂ; ℜz ≤ −α < 0} the Sufficient Condition for Uniform Asymptotic Stability of LTV System ẋ = A(t)x?

“…For the last achievements and research directions on the field of stabilizability of the linear control systems, see, for example, Refs. [24][25][26][27] and the references therein.…”