𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the metric complexity of continuous-time systems

✍ Scribed by Le Yi Wang; Lin Lin

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
531 KB
Volume
6
Category
Article
ISSN
1049-8923

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, metric complexities of certain classes of continuous-time systems are studied, using the time-domain sampling approach and the concepts of Kolmogorov, Gel'fand and sampling n-widths for certain classes of Sobolev space. A sampling theorem is obtained which extends Shannon's sampling theorem to systems with possibly non-band-limited spectra. The theorem demonstrates that continuoustime systems in certain Sobolev spaces can be approximately reconstructed causally from their sampled systems. The Kolmogorov, Gel'fand and sampling n-widths of various uncertainty sets in the Sobolev spaces are derived. The results show that the sampling approach is in fact asymptotically optimal, when the sampling interval is selected to minimize the loss of information in the sampling process, for the modelling of systems in such Sobolev spaces.

πŸ“œ SIMILAR VOLUMES

Modeling of continuous time systems usin
Modeling of continuous time systems using a discrete time representation
✍ J. Schoukens πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 374 KB

Al~traet--The problem of the representation of continuous time systems by difference equations is studied. A solution is proposed using a sample integration technique. The convolution integrals are approximated by digital filters resulting in an arbitrary high accuracy in a wide frequency band.

On the Relations Between Discrete and Co
On the Relations Between Discrete and Continuous Complexity Theory
✍ Klaus Meer πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 389 KB

A b s t r a c t . Relations between discrete and continuous complexity models are considered. The present paper is devoted to combine both models. In particular we analyze the 3-Satisfiability problem. The existence of fast decision procedures for this problem over the reds is examined based on cert