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On l ∞ and l 2 robustness of spatially invariant systems
Author(s) -
Sarwar Azeem,
Voulgaris Petros G.,
Salapaka Srinivasa M.
Publication year - 2010
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.1448
Subject(s) - robustness (evolution) , nonlinear system , invariant (physics) , lti system theory , spectral radius , mathematics , linear system , control theory (sociology) , computer science , mathematical analysis , physics , eigenvalues and eigenvectors , artificial intelligence , control (management) , mathematical physics , biochemistry , chemistry , quantum mechanics , gene
We consider spatiotemporal systems and study their l ∞ and l 2 robustness properties in the presence of spatiotemporal perturbations. In particular, we consider spatially invariant nominal models and provide necessary and sufficient conditions for system robustness for the cases when the underlying perturbations are linear spatiotemporal varying, and nonlinear spatiotemporal invariant, unstructured or structured. It turns out that these conditions are analogous to the scaled small gain condition (which is equivalent to a spectral radius condition and a linear matrix inequality for the l ∞ and l 2 cases, respectively) derived for standard linear time‐invariant models subject to time‐varying linear and time‐invariant nonlinear perturbations. Copyright © 2009 John Wiley & Sons, Ltd.