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On the circle criterion for boundary control systems in factor form : Lyapunov stability and Lur’e equations

Piotr GrabowskiFrank M. Callier — 2006

ESAIM: Control, Optimisation and Calculus of Variations

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...

On the circle criterion for boundary control systems in factor form: Lyapunov stability and Lur'e equations

Piotr GrabowskiFrank M. Callier — 2005

ESAIM: Control, Optimisation and Calculus of Variations

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...

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