Abstract
Summary. In extending the solvability of the output regulation problem to encompass more general classes of time-varying exogenous systems, various non-equivalent definitions of observability play a crucial role in the definition and properties of immersion mappings establishing the so-called “internal model property.” This paper proposes a classification of the immersion mappings based on the underlying observability property, and describes the connections between different canonical realizations of internal models that fully exploit such properties for robust and adaptive output regulation design in periodic systems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
S. Bittanti and P. Bolzern. Stabilizability and detectability of linear periodic systems. Systems & Control Letters, 6(2):141–145, 1985.
S. Bittanti, P. Colaneri, and G. Guardabassi. H-controllability and observability of linear periodic systems. SIAM J. Contr. Optimization, 22(6):889–93, 1984.
C.I. Byrnes and A. Isidori. Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation. IEEE Trans. on Automat. Contr., 48(10):1712–1723, 2003.
C.I. Byrnes and A. Isidori. Nonlinear internal models for output regulation. IEEE Trans. on Automat. Contr., 49(12):2244–2247, 2004.
C.-T. Chen. Linear System Theory and Design. Holt, Rinehart, and Winston, New York, NY, 1984.
G. De Nicolao, G. Ferrari-Trecate, and S. Pinzoni. Zeros of continuous-time linear periodic systems. Automatica, 34(12):1651–1655, 1998.
F. Delli Priscoli. Output regulation with nonlinear internal models. Systems & Control Letters, 53(3-4):177–185, 2004.
M. Farkas. Periodic Motions. Springer Verlag, New York, NY, 1994.
B.A. Francis. The linear multivariable regulator problem. SIAM J. Contr. Optimization, 15(3):486–505, 1977.
J. Huang and Z. Chen. A general framework for tackling the output regulation problem. IEEE Trans. on Automat. Contr., 49(12):2203–2218, 2004.
A. Serrani and A. Isidori. Global robust output regulation for a class of nonlinear systems. Systems & Control Letters, 39(2):133–139, 2000.
A. Serrani, A. Isidori, and L. Marconi. Semi-global nonlinear output regulation with adaptive internal model. IEEE Trans. on Automat. Contr., 46(8):1178–1194, 2001.
L. Silverman. Transformation of time-variable systems to canonical (phase-variable) form. IEEE Trans. on Automat. Contr., 11(2):300–303, 1966.
L. Silverman. Synthesis of impulse response matrices by internally stable and passive realizations. IEEE Trans. Circuit Theory, 15(3):238–245, 1968.
L.M. Silverman and B.D.O Anderson. Controllability, observability and stability of linear systems. SIAM J. Contr. Optimization, 6(1):121–130, 1968.
L.M. Silverman and H.E. Meadows. Controllability and observability in time-variable linear systems. SIAM J. Contr. Optimization, 5(1):64–73, 1967.
L. Weiss and P.L. Falb. Doležal’s theorem, linear algebra with continuously parametrized elemens, and time-varying system. Math. Syst. Theory, 3:67–75, 1969.
Y. Yuksel and J. Bongiorno Jr. Observers for linear multivariable systems with applications. IEEE Trans. on Automat. Contr., 16(6):603–613, 1971.
Z. Zhang and A. Serrani. The linear periodic output regulation problem. Systems & Control Letters, 55(7):518–529, 2006.
Z. Zhang and A. Serrani. Robust regulation with adaptive periodic internal models. Proc. of the 45rd IEEE Conf. on Decision and Contr., 2006.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Serrani, A. (2008). A Taxonomy for Time-Varying Immersions in Periodic Internal-Model Control. In: Astolfi, A., Marconi, L. (eds) Analysis and Design of Nonlinear Control Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74358-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-74358-3_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74357-6
Online ISBN: 978-3-540-74358-3
eBook Packages: EngineeringEngineering (R0)