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Approximating the spectral radius of sets of matrices in the max-algebra is NP-hard

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3 Author(s)
V. D. Blondel ; Div. of Appl. Math., Univ. Catholique de Louvain, Belgium ; S. Gaubert ; J. N. Tsitsiklis

The lower and average spectral radii measure, respectively, the minimal and average growth rates of long products of matrices taken from a finite set. The logarithm of the average spectral radius is traditionally called the Lyapunov exponent. When one performs these products in the max-algebra, we obtain quantities that measure the performance of discrete event systems. We show that approximating the lower and average max-algebraic spectral radii is NP-hard

Published in:

IEEE Transactions on Automatic Control  (Volume:45 ,  Issue: 9 )