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)
On characterizations of the input-to-state stability property. (English) Zbl 0877.93121
Summary: We show that the well-known Lyapunov sufficient condition for “input-to-state stability” (ISS) is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.

93D25Input-output approaches to stability of control systems
93C10Nonlinear control systems
Full Text: DOI
[1] Z.-P. Jiang, A. Teel and L. Praly, Small gain theorem for ISS systems and applications, to appear in: Math. Control Signals Systems. · Zbl 0836.93054
[2] Lin, Y.; Sontag, E. D.; Wang, Y.: A smooth converse Lyapunov theorem for robust stability. IMA preprint # 1192 (1993) · Zbl 0856.93070
[3] Praly, L.; Jiang, Z. -P.: Stabilization by output feedback for systems with ISS inverse dynamics. Systems control lett. 21, 19-34 (1993) · Zbl 0784.93088
[4] Sontag, E. D.: Smooth stabilization implies coprime factorization. IEEE trans. Automat. control 34, 435-443 (1989) · Zbl 0682.93045
[5] Sontag, E. D.: Some connections between stabilization and factorization. Proc. IEEE conf. Decision and control, 990-995 (1989)
[6] Sontag, E. D.: Further facts about input to state stabilization. IEEE trans. Automat. control 35, 473-476 (1990) · Zbl 0704.93056
[7] Tsinias, J.: Sontag’s ”input to state stability condition” and global stabilization using state detection. Systems control lett. 20, 219-226 (1993) · Zbl 0768.93063
[8] Tsinias, J.: Versions of sontag’s input to state stability condition and the global stabilizability problem. SIAM J. Control optim. 31, 928-941 (1993) · Zbl 0788.93076