This article is cited in 6 papers

Linear Systems

On partial stability and detectability of functional differential systems with aftereffect

V. I. Vorotnikov

Sochi Institute of the Peoples’ Friendship University of Russia, Sochi, Russia

Abstract: We consider a general class of the nonlinear non-stationary system of functional differential equations with aftereffect that admits a “partial” (with respect to a part of the variables) zero equilibrium position. We obtain conditions under which stability (asymptotic stability) with respect to a part of the variables of the “partial” equilibrium position implies its stability (asymptotic stability) in all variables. We analyze these conditions from the standpoint of the problem of partial detectability of the system in question and introduce the concept of its partial zero dynamics. We also study an application to the problem of partial stabilization of controllable systems.

Keywords: nonlinear nonstationary system of functional differential equations with aftereffect (delay), partial stability, partial detectability, partial zero dynamics.

Presented by the member of Editorial Board: M. M. Khrustalev

Received: 14.03.2019
Revised: 25.06.2019
Accepted: 18.07.2019

DOI: 10.31857/S0005231020020014

 English version: Automation and Remote Control, 2020, 81:2, 199–210

Bibliographic databases:

• 
• 
•