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Stability radii of linear discrete‐time systems and symplectic pencils
Author(s) -
Hinrichsen D.,
Son N. K.
Publication year - 1991
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.4590010204
Subject(s) - symplectic geometry , computation , discrete time and continuous time , symplectic matrix , pencil (optics) , robustness (evolution) , matrix pencil , mathematics , perturbation (astronomy) , linear system , stability (learning theory) , pure mathematics , control theory (sociology) , mathematical analysis , physics , computer science , algorithm , symplectic manifold , symplectic representation , eigenvalues and eigenvectors , quantum mechanics , chemistry , biochemistry , statistics , machine learning , gene , control (management) , artificial intelligence
In this paper, we introduce and analyse robustness measures for the stability of discrete‐time system x ( t + 1) = Ax ( t ) under parameter perturbations of the form A → A + BDC where B,C are given matrices. In particular we characterize the stability radius of the uncertain system x ( t + 1) = ( A + BDC ) x ( t ), D an unknown complex perturbation matrix, via an associated symplectic pencil and present an algorithm for the computation of that radius.