Stabilization of bilinear oscillating systems with two degrees of freedom
type: Item
instance of: scholarly article
title: Stabilization of bilinear oscillating systems with two degrees of freedom
zbMATH Open document ID: 1025.93024
author: V. V. Alexandrov
author: Kh. Torres Khakome
published in: Moscow University Mechanics Bulletin
publication date: 1999-03-15T00:00:00Z
review text: The authors treat the bilinear oscillating system with two degrees of freedom \[ \begin{aligned} &\ddot x_i + (\omega^2_i + u_1)x_i = u_2,\qquad i = 1,2,\\ &u_i(\cdot)\in U_i = \{u_i(\cdot)\in KC^1\: |u_i(t)|\leq \nu_i\}. \end{aligned}\tag{1} \] The piecewise linear functions of the scalar argument \(s\) \[ u_i = \nu_i \widetilde{\operatorname{sign}} s_i = \begin{cases} \frac{\nu_i}{\delta} s_i &\quad\text{for }|s_i|\leq\delta,\\ \nu_i \operatorname{sign} s_i &\quad\text{for } |s_i|>\delta \end{cases} \] are used as the controls. The problem of system (1) stabilization is studied for two cases: \(\omega_1\neq\omega_2\) and \(\omega_1=\omega_2=\omega_0\).
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 1261630
zbMATH Keywords: bilinear oscillating system
zbMATH Keywords: stabilization
zbMATH Keywords: input saturation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1261630