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Robust stability for singularly perturbed systems with structured state space uncertainties
Author(s) -
Mukaidani Hiroaki,
Mizukami Koichi
Publication year - 2000
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/1520-6416(200009)132:4<62::aid-eej8>3.0.co;2-l
Subject(s) - control theory (sociology) , lyapunov function , mathematics , perturbation (astronomy) , bounded function , singular perturbation , norm (philosophy) , stability (learning theory) , state space , robust control , exponential stability , control system , computer science , nonlinear system , mathematical analysis , control (management) , engineering , physics , electrical engineering , quantum mechanics , statistics , artificial intelligence , machine learning , political science , law
Abstract This paper considers the robust stability of singularly perturbed systems with structured state space uncertainties. By making use of the Lyapunov stability criterion and combining it with the Lyapunov equations, a new approach for deciding a robust stability for uncertain linear singularly perturbed systems is presented. Based on the assumption that the reduced nominal system is stable, we also derive some sufficient conditions for robust stability. Some analytical methods and the Bellman–Gronwall inequality are used to investigate such sufficient conditions. In this paper, it is worth pointing out that we do not need to investigate both the slow system and the fast system by means of the singular perturbation methods because the proposed method is very direct. Furthermore, we only assume that the uncertainties are norm‐bounded. Therefore, the robust stability condition derived here is less conservative than those reported in the control literature. A numerical example is given to demonstrate the validity of our new results. © 2000 Scripta Technica, Electr Eng Jpn, 132(4): 62–72, 2000