zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Sampling and control of switched linear systems. (English) Zbl 1064.94566
Summary: We address the sampling and control issues for switched linear systems. Under synchronous switching and piecewise constant control, a continuous-time switched system is naturally related to a discrete-time sampled-data system. We prove that, with almost any sampling rate, the controllable subspace will be preserved for a switched linear system. We also investigate the possibility of achieving controllability using regular switching mechanisms. We show that, to achieve controllability for a switched linear system, it is sufficient to use cyclic and synchronous switching paths and constant control laws.

94C10Switching theory, application of Boolean algebra; Boolean functions
93C05Linear control systems
Full Text: DOI
[1] Decarlo, R. A.; Branicky, M. S.; Pettersson, S.; Lennartson, B.: Perspective and results on the stability and stabilizability of hybrid systems. Proc. IEEE 88, No. 7, 1069-1082 (2000)
[2] Liberzon, D.; Morse, A. S.: Basic problems in stability and design of switched systems. IEEE control systems 19, No. 5, 59-70 (1999)
[3] Loparo, K. A.; Aslanis, J. T.; Iiajek, O.: Analysis of switching linear systems in the plain, part 2, global behavior of trajectories, controllability and attainability. J. optim. Theory appl. 52, No. 3, 395-427 (1987) · Zbl 0586.93033
[4] X. Xu, P. Antsaklis, On the reachability of a class of second-order switched systems, Technical Report ISIS-99-003, University of Notre Dame, 1999.
[5] Ezzine, J.; Haddad, A. H.: Controllability and observability of hybrid systems. Int. J. Control 49, No. 6, 2045-2055 (1989) · Zbl 0683.93011
[6] Bemporad, A.; Ferrari-Trecate, G.; Morari, M.: Observability and controllability of piecewise affine and hybrid systems. IEEE trans. Automat. control 45, No. 10, 1864-1876 (2000) · Zbl 0990.93010
[7] Sun, Z.; Ge, S. S.; Lee, T. H.: Reachability and controllability criteria for switched linear systems. Automatica 38, No. 5, 775-786 (2002) · Zbl 1031.93041
[8] Xie, G. M.; Wang, L.: Controllability and stabilizability of switched linear-systems. Systems control lett. 48, No. 2, 135-155 (2003) · Zbl 1134.93403
[9] Blondel, V. D.; Tsitsiklis, J. N.: Complexity of stability and controllability of elementary hybrid systems. Automatica 35, No. 3, 479-489 (1999) · Zbl 0943.93044
[10] Standord, D. P.: Stability for a multi-rate sampled-data system. SIAM J. Control optim. 17, 390-399 (1979) · Zbl 0439.93041
[11] Stanford, D. P.; Jr., L. T. Conner: Controllability and stabilizability in multi-pair systems. SIAM J. Control optim. 18, No. 5, 488-497 (1980) · Zbl 0454.93008
[12] Jr., L. T. Conner; Stanford, D. P.: State deadbeat response and obsevability in multi-modal systems. SIAM J. Control optim. 22, No. 4, 630-644 (1984) · Zbl 0549.93036
[13] Wonham, W. M.: Linear multivariable control --- A geometric approach. (1979) · Zbl 0424.93001
[14] Ge, S. S.; Sun, Z.; Lee, T. H.: Reachability and controllability of switched linear discrete-time systems. IEEE trans. Automat. control 46, No. 9, 1437-1441 (2001) · Zbl 1031.93028
[15] Fliess, M.: Reversible linear and nonlinear discrete-time dynamics. IEEE trans. Automat. control 37, No. 8, 1144-1153 (1992) · Zbl 0764.93058
[16] Troch, I.: Comments on `driving a linear constant system by piecewise constant control’. Int. J. Systems sci. 21, No. 11, 2379-2386 (1990) · Zbl 0723.93005