8 research outputs found
An Overview of Transience Bounds in Max-Plus Algebra
We survey and discuss upper bounds on the length of the transient phase of
max-plus linear systems and sequences of max-plus matrix powers. In particular,
we explain how to extend a result by Nachtigall to yield a new approach for
proving such bounds and we state an asymptotic tightness result by using an
example given by Hartmann and Arguelles.Comment: 13 pages, 2 figure
Generalizations of Bounds on the Index of Convergence to Weighted Digraphs
We study sequences of optimal walks of a growing length, in weighted
digraphs, or equivalently, sequences of entries of max-algebraic matrix powers
with growing exponents. It is known that these sequences are eventually
periodic when the digraphs are strongly connected. The transient of such
periodicity depends, in general, both on the size of digraph and on the
magnitude of the weights. In this paper, we show that some bounds on the
indices of periodicity of (unweighted) digraphs, such as the bounds of
Wielandt, Dulmage-Mendelsohn, Schwarz, Kim and Gregory-Kirkland-Pullman, apply
to the weights of optimal walks when one of their ends is a critical node.Comment: 17 pages, 3 figure
Entropy of regular timed languages
For timed languages, we define size measures: volume for languages with a fixed finite number of events, and entropy (growth rate) as asymptotic measure for an unbounded number of events. These measures can be used for quantitative comparison of languages, and the entropy can be viewed as information contents of a timed language. For languages accepted by deterministic timed automata, we give exact formulas for volumes. We show that automata with non-vanishing entropy ("thick") have a normal (non-Zeno, discretizable etc.) behavior for typical runs. Next, we characterize the entropy, using methods of functional analysis, as the logarithm of the leading eigenvalue (spectral radius) of a positive integral operator. We devise a couple of methods to compute the entropy: a symbolical one for so-called "1 1 ⁄2-clock" automata, and a numerical one (with a guarantee of convergence)
Discrete Time Systems
Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area