This article has an erratum: [erratum]
Volume 12, Number 1, January 2006
|Page(s)||169 - 197|
|Published online||15 December 2005|
On the circle criterion for boundary control systems in factor form: Lyapunov stability and Lur'e equations
Institute of Automatics, AGH University of Science and Technology,
avenue A. Mickiewicz 30, B1, rm.314, 30-059 Cracow, Poland; email@example.com
2 University of Namur (FUNDP), Department of Mathematics, Rempart de la Vierge 8, 5000 Namur, Belgium; firstname.lastname@example.org
Revised: 6 January 2005
Revised: 23 February 2005
A Lur'e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur'e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on results by Oostveen and Curtain [Automatica 34 (1998) 953–967]. All the results are illustrated in detail by an electrical transmission line example of the distortionless loaded -type. The paper uses extensively the philosophy of reciprocal systems with bounded generating operators as recently studied and used by Curtain in (2003) [Syst. Control Lett. 49 (2003) 81–89; SIAM J. Control Optim. 42 (2003) 1671–1702].
Mathematics Subject Classification: 34G / 35A / 47D / 93B
Key words: Infinite-dimensional control systems / semigroups / Lyapunov functionals / circle criterion.
© EDP Sciences, SMAI, 2006
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.