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Corrigendum to: “On the circle criterionfor boundary control systems in factor form: Lyapunov stabilityand Lur'e equations”
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 15 / Issue 3 / July 2009
- Published online by Cambridge University Press:
- 18 June 2009, pp. 741-744
- Print publication:
- July 2009
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- Article
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On the circle criterionfor boundarycontrol systemsin factor form: Lyapunov stability and Lur'e equations
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 12 / Issue 1 / January 2006
- Published online by Cambridge University Press:
- 15 December 2005, pp. 169-197
- Print publication:
- January 2006
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- Article
- Export citation
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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 [Automatica34 (1998) 953–967]. All theresults are illustrated in detail by an electrical transmission line example of thedistortionless loaded $\mathfrak{RLCG}$
-type. The paper uses extensively thephilosophy of reciprocal systems with bounded generating operators as recentlystudied and used by Curtain in (2003) [Syst. Control Lett.49 (2003) 81–89; SIAM J. Control Optim.42 (2003) 1671–1702].
