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On the calculation of time‐varying stability radii
Author(s) -
Wirth Fabian
Publication year - 1998
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/(sici)1099-1239(1998100)8:12<1043::aid-rnc364>3.0.co;2-h
Subject(s) - spectral radius , mathematics , radius , lyapunov exponent , stability (learning theory) , convergence (economics) , optimal control , rate of convergence , exponent , discrete time and continuous time , value (mathematics) , mathematical analysis , control theory (sociology) , mathematical optimization , control (management) , nonlinear system , computer science , eigenvalues and eigenvectors , statistics , physics , computer network , channel (broadcasting) , linguistics , computer security , philosophy , quantum mechanics , machine learning , economics , economic growth , artificial intelligence
The problem of calculating the maximal Lyapunov exponent (generalized spectral radius) of a discrete inclusion is formulated as an average yield optimal control problem. It is shown that the maximal value of this problem can be approximated by the maximal value of discounted optimal control problems, where for irreducible inclusions the convergence is linear in the discount rate. This result is used to obtain convergence rates of an algorithm for the calculation of time‐varying stability radii. © 1998 John Wiley & Sons, Ltd.