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)
Feedback passivity of nonlinear discrete-time systems with direct input-output link. (English) Zbl 1077.93045
This paper deals with the passification problem for nonlinear, discrete-time systems of the form $$x(k+1)= f(x(k), u(k)),\quad y(k)= h(x(k),u(k)),$$ where $f$ and $h$ are smooth maps vanishing at $x= u= 0$. The main result asserts that if the relative degree of the system is zero and there exist locally passive zero dynamics with a positive definite storage function of class $C^2$, then the system can be rendered passive by applying a regular feedback. The case of affine systems is considered with special attention.

93D15Stabilization of systems by feedback
93C55Discrete-time control systems
93D25Input-output approaches to stability of control systems
Full Text: DOI
[1] Byrnes, C. I.; Isidori, A.; Willems, J. C.: Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE transactions on automatic control 36, 1228-1240 (1991) · Zbl 0758.93007
[2] Byrnes, C. I., & Lin, W. (1993). Discrete-time lossless systems, feedback equivalence, and passivity. Proceedings of the IEEE 32nd conference on decision and control, San Antonio, Texas (pp. 1775-1781).
[3] Byrnes, C. I.; Lin, W.: Losslessness, feedback equivalence, and the global stabilization of discrete-time nonlinear systems. IEEE transactions on automatic control 39, No. 1, 83-98 (1994) · Zbl 0807.93037
[4] Lin, W. (1993). Synthesis of discrete-time nonlinear systems. Ph.D. thesis, Washington University, USA.
[5] Monaco, S., & Normand-Cyrot, D. (1987). Minimum-phase nonlinear discrete-time systems and feedback stabilization. Proceedings of the 26th conference on decision and control, Los Angeles (pp. 979-986). · Zbl 0625.93013
[6] Monaco, S.; Normand-Cyrot, D.: Zero dynamics of sampled nonlinear systems. Systems and control letters 11, 229-234 (1988) · Zbl 0664.93037
[7] Monaco, S., & Normand-Cyrot, D. (1999). Nonlinear representations and passivity conditions in discrete time. In Robustness in identification and control. Lecture notes in control and information sciences, Vol. 245 (pp. 422-433). Berlin: Springer. · Zbl 0948.93518
[8] Navarro-López, E. M. (2002). Dissipativity and passivity-related properties in nonlinear discrete-time systems. Ph.D. thesis, Universitat Politècnica de Catalunya, Barcelona, Spain. ISBN: 84-688-1941-7.
[9] Navarro-López, E. M., & Fossas-Colet, E. (2002). Dissipativity, passivity and feedback passivity in the nonlinear discrete-time setting. 15th IFAC world congress, Barcelona, Spain. · Zbl 1293.93614
[10] Navarro-López, E. M., Fossas-Colet, E., & Cortés, D. (2002a). Local feedback dissipativity and dissipativity-based stabilization of nonlinear discrete-time systems. Latin American conference on automatic control, Guadalajara, Mexico. · Zbl 1293.93614
[11] Navarro-López, E. M.; Sira-Ramı\acute{}rez, H.; Fossas-Colet, E.: Dissipativity and feedback dissipativity properties of general nonlinear discrete-time systems. European journal of control. Special issue: dissipativity of dynamical systems. Application in control 8, No. 3, 265-274 (2002) · Zbl 1293.93614
[12] Willems, J. C.: Dissipative dynamical systems. Part I: general theory. Part iilinear systems with quadratic supply rates. Archive for rational mechanics and analysis 45, No. 5, 321, 351, 352.393 (1972)