zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Controllability analysis of linear time-varying systems with multiple time delays and impulsive effects. (English) Zbl 1238.93016
Summary: The issue of controllability for linear time-varying systems with multiple time delays in the control and impulsive effects is addressed. The solution of such systems based on the variation of parameters is derived. Several sufficient and necessary algebraic conditions for two kinds of controllability, i.e., controllability to the origin and controllability, are derived. The relation among these conditions are established. A numerical example is provided to illustrate the effectiveness of the proposed methods.
MSC:
93B05Controllability
93C23Systems governed by functional-differential equations
34K45Functional-differential equations with impulses
References:
[1]Li, Z. G.; Wen, C. Y.; Soh, Y. C.: Analysis and design of impulsive control systems, IEEE trans. Automat. control 46, 894-899 (2001) · Zbl 1001.93068 · doi:10.1109/9.928590
[2]Liu, Y.; Zhao, S. W.: A new approach to practical stability of impulsive functional differential equations in terms of two measures, J. comput. Appl. math. 223, 449-458 (2009) · Zbl 1162.34065 · doi:10.1016/j.cam.2008.01.029
[3]Leela, S.; Mcrae, F. A.; Sivasundaram, S.: Controllability of impulsive differential equations, J. math. Anal. appl. 177, 24-30 (1993) · Zbl 0785.93016 · doi:10.1006/jmaa.1993.1240
[4]Sakthivel, R.; Anandhi, E. R.: Approximate controllability of impulsive differential equations with state-dependent delay, Internat. J. Control 83, No. 2, 387-393 (2010) · Zbl 1184.93021 · doi:10.1080/00207170903171348
[5]George, R. K.; Nandakumaran, A. K.; Arapostathis, A.: A note on controllability of impulsive systems, J. math. Anal. appl. 241, No. 2, 276-283 (2000) · Zbl 0965.93015 · doi:10.1006/jmaa.1999.6632
[6]Sun, Z. D.; Ge, S. S.; Lee, T. H.: Controllability and reachability criteria for switched linear systems, Automatica 38, 775-786 (2002) · Zbl 1031.93041 · doi:10.1016/S0005-1098(01)00267-9
[7]Medina, E. A.; Lawrence, D. A.: Reachability and observability of linear impulsive systems, Automatica 44, 1304-1309 (2008)
[8]Sussmann, H. J.; Jurdjevic, V.: Controllability of nonlinear systems, J. differential equations 12, 95-116 (1972) · Zbl 0242.49040 · doi:10.1016/0022-0396(72)90007-1
[9]Chang, Y. K.; Li, W. T.; Nieto, J. J.: Controllability of evolution differential inclusions in Banach spaces, Nonlinear anal. TMA. 67, 623-632 (2007) · Zbl 1128.93005 · doi:10.1016/j.na.2006.06.018
[10]Rugh, W. J.: Linear systems theory, (1993)
[11]Xie, G. M.; Wang, L.: Controllability and observability of a class of linear impulsive systems, J. math. Anal. appl. 304, 336-355 (2005) · Zbl 1108.93022 · doi:10.1016/j.jmaa.2004.09.028
[12]Guan, Z. H.; Qian, T. H.; Yu, X. H.: On controllability and observability for a class of impulsive systems, Systems control lett. 47, 247-257 (2002) · Zbl 1106.93305 · doi:10.1016/S0167-6911(02)00204-9
[13]Guan, Z. H.; Qian, T. H.; Yu, X. H.: Controllability and observability of linear time-varying impulsive systems, IEEE trans. Circuits syst. I 49, 1198-1208 (2002)
[14]Zhao, S. W.; Sun, J. T.: Controllability and observability for a class of time-varying impulsive systems, Nonlinear anal. RWA. 10, 1370-1380 (2009) · Zbl 1159.93315 · doi:10.1016/j.nonrwa.2008.01.012
[15]Liu, B.; Marquez, H. J.: Controllability and observability for a class of controlled switching impulsive systems, IEEE trans. Automat. control 53, 2360-2366 (2008)
[16]Zhao, S. W.; Sun, J. T.: Controllability and observability for time-varying switched impulsive controlled systems, Internat. J. Robust nonlinear control 20, 1313-1325 (2010) · Zbl 1206.93019 · doi:10.1002/rnc.1510
[17]Klamka, J.: Stochastic controllability of systems with multiple delays in control, Internat. J. Appl. math. Comput. sci. 19, 39-47 (2009) · Zbl 1169.93005 · doi:10.2478/v10006-009-0003-9
[18]Umana, R. A.: Null controllability of nonlinear infinite neutral systems with multiple delays in control, J. comput. Anal. appl. 10, 509-522 (2008) · Zbl 1132.93010
[19]Sikora, B.: On constrained controllability of dynamical systems with multiple delays in control, Appl. math., Warsaw 32, 87-101 (2005) · Zbl 1079.93009 · doi:10.4064/am32-1-7
[20]Zhang, H.; Duan, G.; Xie, L.: Linear quadratic regulation for linear time-varying systems with multiple input delays, Automatica 42, No. 9, 1465-1476 (2006) · Zbl 1128.49304 · doi:10.1016/j.automatica.2006.04.007
[21]Cui, P.; Zhang, C.; Zhang, H.; Zhao, H.: Indefinite linear quadratic optimal control problem for singular discrete-time system with multiple input delays, Automatica 45, No. 10, 2458-2461 (2009) · Zbl 1183.49033 · doi:10.1016/j.automatica.2009.06.018
[22]Chyung, D. H.: On the controllability of linear systems with delay in control, IEEE trans. Automat. control 15, 694-695 (1970)
[23]Sebakhy, O.; Bayoumi, M. M.: Controllability of linear time-varying systems with delay in control, Internat. J. Control 17, No. 1, 127-135 (1972) · Zbl 0247.93004 · doi:10.1080/00207177308932363
[24]G.M. Xie, J.Y. Yu, L. Wang, Necessary and sufficient conditions for controllability of switched impulsive control systems with time delay, in: Proc. 45th IEEE Conf. Decision and Control 2006 pp. 4093–4098.
[25]Lee, E. B.; Markus, L.: Foundations of optimal control theory, (1986)
[26]Sun, Y.; Nelson, P. W.; Ulsoy, A. G.: Controllability and observability of systems of linear delay differential equations via the matrix Lambert W function, IEEE trans. Automat. control 53, 854-860 (2008)
[27]Liu, Y.; Zhao, S. W.: Controllability for a class of linear time-varying impulsive systems with time delay in control input, IEEE trans. Automat. control 56, 395-399 (2011)
[28]Balachandran, K.; Dauer, J. P.: Null controllability of nonlinear infinite delay systems with time varying multiple delays in control, Appl. math. Lett. 9, 115-121 (1996) · Zbl 0856.93011 · doi:10.1016/0893-9659(96)00042-0