| Title:
|
Controllability and observability of time-invariant linear dynamic systems (English) |
| Author:
|
Bohner, Martin |
| Author:
|
Wintz, Nick |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
137 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
149-163 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle. (English) |
| Keyword:
|
time scale |
| Keyword:
|
dynamic equation |
| Keyword:
|
exponential function |
| Keyword:
|
controllability |
| Keyword:
|
reachability |
| Keyword:
|
observability |
| Keyword:
|
duality principle |
| Keyword:
|
time invariance |
| MSC:
|
34A30 |
| MSC:
|
34H05 |
| MSC:
|
34N05 |
| MSC:
|
93B05 |
| MSC:
|
93B07 |
| idZBL:
|
Zbl 1265.34334 |
| idMR:
|
MR2978261 |
| DOI:
|
10.21136/MB.2012.142861 |
| . |
| Date available:
|
2012-06-08T10:08:40Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142861 |
| . |
| Reference:
|
[1] Aulbach, B., Hilger, S.: A unified approach to continuous and discrete dynamics.Colloq. Math. Soc. János Bolyai. 53 (1990), 37-56. Zbl 0723.34030, MR 1062633 |
| Reference:
|
[2] Bartosiewicz, Z., Pawłuszewicz, E.: Linear control systems on time scales: unification of continuous and discrete.Proc. of 10th IEEE Int. Conference MMAR. (2004), 263-266. MR 2323260 |
| Reference:
|
[3] Bartosiewicz, Z., Pawłuszewicz, E.: Realizations of linear control systems on time scales.Control Cybernet. 35 (2006), 769-786. Zbl 1133.93033, MR 2323260 |
| Reference:
|
[4] Bohner, M., Peterson, A.: Dynamic Equations on Time Scales.Birkhäuser, Basel (2001). Zbl 0993.39010, MR 1843232 |
| Reference:
|
[5] Bohner, M., Peterson, A., eds.: Advances in Dynamic Equations on Time Scales.Birkhäuser, Boston, MA (2003). Zbl 1025.34001, MR 1962542 |
| Reference:
|
[6] DaCunha, J.: Transition matrix and generalized matrix exponential via the Peano-{B}aker series.J. Difference Equ. Appl. 11 (2005), 1245-1264. Zbl 1093.39017, MR 2191005, 10.1080/10236190500272798 |
| Reference:
|
[7] Davis, J. M., Gravagne, I. A., Jackson, B. J., II, R. J. Marks: Controllability, observability, realizability, and stability of dynamic linear systems.Electron. J. Diff. Equ. 37 (2009), 1-32. MR 2495842 |
| Reference:
|
[8] Fausett, L. V., Murty, K. N.: Controllability, observability and realizability criteria on time scale dynamical systems.Nonlinear Stud. 11 (2004), 627-638. MR 2100755 |
| Reference:
|
[9] Hilscher, R., Zeidan, V.: Weak maximum principle and accessory problem for control problems on time scales.Nonlinear Anal. 70 (2009), 3209-3226. Zbl 1157.49030, MR 2503067 |
| Reference:
|
[10] Kalman, R. E.: Contributions to the theory of optimal control.Bol. Soc. Mat. Mexicana. 2 (1960), 102-119. Zbl 0112.06303, MR 0127472 |
| Reference:
|
[11] Kalman, R. E.: On the general theory of control systems.Proc. 1st IFAC Congress Automatic Control. 1 (1960), 481-492. |
| Reference:
|
[12] Kalman, R. E.: Mathematical description of linear dynamical systems.J. SIAM Control Ser. A Control. 1 (1963), 152-192. Zbl 0145.34301, MR 0152167 |
| Reference:
|
[13] Kalman, R. E., Ho, Y. C., Narendra, K. S.: Controllability of linear dynamical systems.Contrib. Differ. Equ. 1 (1963), 189-213. Zbl 0151.13303, MR 0155070 |
| Reference:
|
[14] Molnar, S., Szigeti, F.: Controllability and reachability of dynamic discrete-time linear systems.Proceedings of the 4th International Conference on Control and Automation (2003), 350-354. MR 1368381 |
| Reference:
|
[15] Wintz, N.: The Kalman filter on time scales.PhD Thesis, Missouri University of Science and Technology, Rolla, Missouri, USA (2009). MR 2941934 |
| Reference:
|
[16] Zafer, A.: The matrix exponential on time scales.ANZIAM J. 48 (2006), 99-106. MR 2263186, 10.1017/S1446181100003436 |
| . |
