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)
Output regulation for nonlinear systems: An overview. (English) Zbl 0962.93007
This survey on robust output regulation (asymptotic tracking, disturbance rejection) via the internal model approach presents first the linear case, which has been treated by Davison, Wonham and Francis, and then results of the authors in the nonlinear case, and mentions the further efforts of Huang, Lin, Khalil (approximation procedure, robustification, semiglobal aspects when the zero dynamics is stable). A section stresses via a linear example that perfect tracking via an inversion procedure is not robust to parametric uncertainties in the system but asymptotic tracking will do. The authors introduce the definitions of “structurally stable output regulation” and the stronger “robust output regulation”, but the latter concept is not developed explicitly here. A last section deals with current research (semiglobal aspects, cases when the dynamics of the exogenous input is uncertain, partial differential equations). It should be mentioned that this publication has not been written with the greatest care. The title without the word “nonlinear” would be more accurate since the linear situation takes almost half of the paper. In Theorem 2, the statement is not valid for all $P$ and $Q$ as written but only locally as expressed earlier. The locations of the input and of the disturbance in (15) and (20) are interchanged. Unfortunately, the dimensions of introduced quantities are omitted sometimes. The transition from the linear to the nonlinear situation is not transparent. The examples are superfluous. Worse, the presentation is quite formal masking the essence of the design: The internal model (for a first compensator) allows to catch the uncertainties in the parameters of the dynamics and in the initial condition of the disturbance dynamics in its initial condition; this leads to a second stabilizing compensator to get rid of it.

93-02Research monographs (systems and control)
93B51Design techniques in systems theory
93C73Perturbations in control systems
Full Text: DOI