| Title:
|
Rational algebra and MM functions (English) |
| Author:
|
Cuninghame-Green, Ray A. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
[123]-128 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
MM functions, formed by finite composition of the operators min, max and translation, represent discrete-event systems involving disjunction, conjunction and delay. The paper shows how they may be formulated as homogeneous rational algebraic functions of degree one, over (max, +) algebra, and reviews the properties of such homogeneous functions, illustrated by some orbit-stability problems. (English) |
| Keyword:
|
algebraic systems theory |
| Keyword:
|
discrete-event dynamicsystems |
| Keyword:
|
asymptotic stability |
| MSC:
|
06F05 |
| MSC:
|
15A80 |
| MSC:
|
93B27 |
| MSC:
|
93C65 |
| MSC:
|
93D20 |
| idZBL:
|
Zbl 1249.93124 |
| idMR:
|
MR1996550 |
| . |
| Date available:
|
2009-09-24T19:51:51Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135514 |
| . |
| Reference:
|
[1] Baccelli F. L., Cohen G., Olsder G.-J., Quadrat J.-P.: Synchronization and Linearity, An Algebra for Discrete Event Systems.Wiley, Chichester 1992 Zbl 0824.93003, MR 1204266 |
| Reference:
|
[2] Cuninghame-Green R. A.: Minimax Algebra (Lecture Notes in Economics and Mathematical Systems 166).Springer–Verlag, Berlin 1979 MR 0580321 |
| Reference:
|
[3] Cuninghame-Green R. A., Meijer P. F. J.: An algebra for piecewise-linear minimax problems.Discrete Appl. Math. 2 (1980), 267–294 Zbl 0448.90070, MR 0600179, 10.1016/0166-218X(80)90025-6 |
| Reference:
|
[4] Cuninghame-Green R. A.: Minimax algebra and applications.In: Advances in Imaging and Electron Physics 90 (P. W. Hawkes, ed.), Academic Press, New York 1995 Zbl 0739.90073 |
| Reference:
|
[5] Cuninghame-Green R. A.: Maxpolynomial equations.Fuzzy Sets and Systems 75 (1995), 179–187 Zbl 0857.90134, MR 1358220, 10.1016/0165-0114(95)00012-A |
| Reference:
|
[6] Gaubert S., Gunawardena J.: The duality theorem for min-max functions.C. R. Acad. Sci. Paris 326 (1998), 43–48 Zbl 0933.49017, MR 1649473, 10.1016/S0764-4442(97)82710-3 |
| Reference:
|
[7] Manber U.: Introduction to Algorithms.Addison–Wesley, New York 1989 Zbl 0825.68397, MR 1091251 |
| . |
