Open AccessStability of perturbed switched homogeneous systems with delays and uncertainties
Author(s) -
Liu Xingwen
Publication year - 2016
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2015.0633
Subject(s) - lipschitz continuity , perturbation (astronomy) , control theory (sociology) , homogeneous , mathematics , differentiable function , exponential stability , stability (learning theory) , exponential growth , mathematical analysis , computer science , control (management) , nonlinear system , physics , quantum mechanics , combinatorics , artificial intelligence , machine learning
This study addresses the stability problem of perturbed switched systems with time‐varying delays and uncertainties. The considered switching signals include five classes and the uncertainties take values on compact sets. It is assumed that the nominal system (perturbation‐free system) is robustly uniformly exponentially stable and that the perturbations satisfy vanishing condition plus one of the following three constraints: being locally Lipschitz at origin, globally Lipschitz, and differentiable at origin. By ‘vanishing’, the authors mean that the perturbation is zero at origin. With these assumptions, it is first revealed that for switched systems being homogeneous of degree one, if the perturbation is sufficiently small, then the perturbed system preserves the stability property of the nominal system, locally or globally, depending on perturbation itself. These results are then applied to switched linear systems with delays, showing that the same conclusion holds for such systems with four types of most frequently encountered uncertainties. Finally, an example is provided to illustrate the proposed theoretical results.