Premium
Robustness of transitions in switched linear systems
Author(s) -
Jönsson Ulf T.
Publication year - 2005
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.987
Subject(s) - robustness (evolution) , affine transformation , parameterized complexity , subspace topology , linear system , quadratic equation , mathematics , control theory (sociology) , lipschitz continuity , nonlinear system , robust control , mathematical optimization , computer science , algorithm , mathematical analysis , control (management) , biochemistry , chemistry , physics , geometry , quantum mechanics , artificial intelligence , pure mathematics , gene
A robustness problem for transitions in switched linear systems is considered in this paper. The specific problem is to estimate the size of the image when a subset of an affine subspace is mapped by an uncertain system to another affine subspace. It is assumed that the system dynamics is linear and that the uncertainty and the disturbances are characterized by integral quadratic constraints (IQC). The estimates can be obtained by solving a special affinely parameterized linear quadratic optimal control problem. The results are applied to the problem of verifying robustness of oscillations in a switched linear system. In particular, sufficient conditions are given, which ensure that there remains a periodic solution when the system is perturbed by a Lipschitz continuous nonlinearity. Copyright © 2005 John Wiley & Sons, Ltd.