Analysis of stability and stabilization of cascade systems with time delay in terms of linear matrix inequalities
- Authors: Druzhinina O.V.1,2, Sedova N.O.1,2
-
Affiliations:
- Federal Research Center Information Science and Control
- Ul’yanovsk State University
- Issue: Vol 56, No 1 (2017)
- Pages: 19-32
- Section: Systems Theory and General Control Theory
- URL: https://journals.rcsi.science/1064-2307/article/view/219791
- DOI: https://doi.org/10.1134/S1064230717010063
- ID: 219791
Cite item
Abstract
The stability of nonlinear cascade systems with a time delay is studied. Conditions of the global asymptotic stability in terms of linear matrix inequalities for a finite set of matrices are obtained. The problem of stabilization of the controlled delay system is considered, which is solved based on the stability conditions. The proposed approach to the analysis of qualitative properties and to the solution of stabilization problems is based on the results concerning the asymptotic stability of the delay linear systems, the decomposition of the original system, and the representation of the delay nonlinear system by a Takagi–Sugeno system. Examples illustrating the simplification of the system analysis by reducing its size and decreasing the number of linear matrix inequalities are discussed.
About the authors
O. V. Druzhinina
Federal Research Center Information Science and Control; Ul’yanovsk State University
Author for correspondence.
Email: ovdruzh@mail.ru
Russian Federation, Moscow; Ul’yanovsk
N. O. Sedova
Federal Research Center Information Science and Control; Ul’yanovsk State University
Email: ovdruzh@mail.ru
Russian Federation, Moscow; Ul’yanovsk