| Title:
|
Controllability of linear impulsive systems – an eigenvalue approach (English) |
| Author:
|
S. Muni, Vijayakumar |
| Author:
|
K. George, Raju |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
727-752 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are provided that demonstrate--for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems. (English) |
| Keyword:
|
eigenvalues |
| Keyword:
|
impulses |
| Keyword:
|
controllability |
| MSC:
|
15A18 |
| MSC:
|
34A37 |
| MSC:
|
93B05 |
| idZBL:
|
Zbl 07286044 |
| idMR:
|
MR4168533 |
| DOI:
|
10.14736/kyb-2020-4-0727 |
| . |
| Date available:
|
2020-10-30T16:27:38Z |
| Last updated:
|
2021-02-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148381 |
| . |
| Reference:
|
[1] Benzaid, Z., Sznaier, M.: Constrained controllability of linear impulse differential systems..IEEE Trans. Automat. Contr. 39(5) (1994), 1064-1066. MR 1274362, |
| Reference:
|
[2] George, R. K., Nandakumaran, A. K., Arapostathis, A.: A note on controllability of impulsive systems..J. Math. Anal. Appl. 241(2) (2000), 276-283. MR 1739206, |
| Reference:
|
[3] Guan, Z. H., Qian, T. H., Yu, X.: Controllability and observability of linear time-varying impulsive systems..IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 49(8) (2002), 1198-1208. MR 1929297, |
| Reference:
|
[4] Guan, Z. H., Qian, T. H., Yu, X.: On controllability and observability for a class of impulsive systems..Systems Control Lett. 47(3) (2002), 247-257. MR 2008278, |
| Reference:
|
[5] Han, J., Liu, Y., Zhao, S., Yang, R.: A note on the controllability and observability for piecewise linear time-varying impulsive systems..Asian J. Control 15(6) (2013), 1867-1870. MR 3130263, |
| Reference:
|
[6] Lakshmikantham, V., Bainov, D. D., Simeonov, P. S.: Theory of impulsive differential equations..World Scientific, Singapore 1989. MR 1082551 |
| Reference:
|
[7] Leela, S., McRae, F. A., Sivasundaram, S.: Controllability of impulsive differential equations..J. Math. Anal. Appl. 177(1) (1993), 24-30. MR 1224802, |
| Reference:
|
[8] Muni, V. S., George, R. K.: Controllability of semilinear impulsive control systems with multiple time delays in control..IMA J. Math. Control \& Inform. 36(3) (2019), 869-899. MR 4009506, |
| Reference:
|
[9] Terrell, W. J.: Stability and stabilization: An introduction..Princeton University Press, Princeton, USA 2009. MR 2482799 |
| Reference:
|
[10] Xie, G., Wang, L.: Controllability and observability of a class of linear impulsive systems..J. Math. Anal. Appl. 304(1) (2005), 336-355. MR 2124666, |
| Reference:
|
[11] Zhao, S., Sun, J.: Controllability and observability for a class of time-varying impulsive systems..Nonlinear Anal. RWA. 10(3) (2009), 1370-1380. MR 2502952, |
| Reference:
|
[12] Zhao, S., Sun, J.: Controllability and observability for impulsive systems in complex fields..Nonlinear Anal. RWA. 11(3) (2010), 1513-1521. MR 2646565, |
| . |
