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

Piotr Grabowski, Frank 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 Grabowski, Frank 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...

On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients

Ludovic Rifford (2001)

ESAIM: Control, Optimisation and Calculus of Variations

Let x ˙ = f ( x , u ) be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke’s generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...

On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients

Ludovic Rifford (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Let x ˙ = f ( x , u ) be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke's generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...

Quadratic stabilization of distributed parameter systems with norm-bounded time-varying uncertainty.

Wanyi Chen, Fengsheng Tu (1997)

Collectanea Mathematica

This note focuses on the study of robust H-sub-infinity control design for a kind of distributed parameter systems in which time-varying norm-bounded uncertainty enters the state and input operators. Through a fixed Lyapunov function, we present a state feedback control which stabilizes the plant and guarantees an H-sub-infinity norm bound on disturbance attenuation for all admissible uncertainties. In the process, we generalize some known results for finite dimensional linear systems.

Quantitative L^{P} stability analysis of a class of linear time-varying feedback systems

Pini Gurfil (2003)

International Journal of Applied Mathematics and Computer Science

The L^{P} stability of linear feedback systems with a single time-varying sector-bounded element is considered. A sufficient condition for L^{P} stability, with 1 ≤ p ≤ ∞, is obtained by utilizing the well-known small gain theorem. Based on the stability measure provided by this theorem, quantitative results that describe output-to-input relations are obtained. It is proved that if the linear time-invariant part of the system belongs to the class of proper positive real transfer functions with a...

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