On the correspondence of hyperbolic geometry and system analysis
| Autor: | Alexandros Soumelidis, Tamás Luspay, István Gőzse, Tamás Péni |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
Pure mathematics Hyperbolic group 020208 electrical & electronic engineering Mathematical analysis Hyperbolic function Hyperbolic manifold 02 engineering and technology Relatively hyperbolic group Inverse hyperbolic function 020901 industrial engineering & automation Control and Systems Engineering 0202 electrical engineering electronic engineering information engineering Hyperbolic angle Hyperbolic triangle Mathematics Hyperbolic equilibrium point |
| Zdroj: | IFAC-Papers |
| ISSN: | 2405-8963 |
| DOI: | 10.1016/j.ifacol.2017.08.917 |
| Popis: | Different aspects of the relation between hyperbolic geometry and linear system theory are discussed in this paper. The underlying connection is presented by an intuitive example that points out the basic motivations. It is shown that the convergence factor of Laguerre series expansion is equal to the hyperbolic distance, under certain conditions. Preliminary results are also reported, connecting the H∞ norm and ν-gap metric with the hyperbolic distance. Furthermore, the equivalence of (i) the H∞ norm of the difference of two first order LTI system, (ii) the ν-gap of these systems and (iii) the hyperbolic distance is also proved, under specified assumptions. |
| Databáze: | OpenAIRE |
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