How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance

George Weiss; Marius Tucsnak

Displaying similar documents to “How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance”

The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation

M. I. Belishev, I. Lasiecka (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input $\to$ state” map in $L_{2}$ -norms is established. A structure of the reachable sets for arbitrary $T > 0$ is studied. In general case, only the first component $u (\cdot, T)$ of the complete state ${u (\cdot, T), u_{t} (\cdot, T)}$ may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data...

On the $L^{p}$ -stabilization of the double integrator subject to input saturation

Yacine Chitour (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a finite-dimensional control system $(Σ) \dot{x} (t) = f (x (t), u (t))$ , such that there exists a feedback stabilizer $k$ that renders $\dot{x} = f (x, k (x))$ globally asymptotically stable. Moreover, for $(H, p, q)$ with $H$ an output map and $1 \leq p \leq q \leq \infty$ , we assume that there exists a $𝒦_{\infty}$ -function $α$ such that $∥ H (x_{u}) ∥_{q} \leq {α (∥ u ∥}_{p})$ , where $x_{u}$ is the maximal solution of ${(Σ)}_{k} \dot{x} (t) = f (x (t), k (x (t)) + u (t))$ , corresponding to $u$ and to the initial condition $x (0) = 0$ . Then, the gain function $G_{(H, p, q)}$ of $(H, p, q)$ given by $G_{(H, p, q)} (X) \overset{def}{=} sup_{{∥ u ∥}_{p} = X} {∥ H (x_{u}) ∥}_{q},$ is well-defined. We call profile of $k$ for $(H, p, q)$ any $𝒦_{\infty}$ -function which is of the same order of...

Dynamic stabilization of systems via decoupling techniques

Farid Ammar-Khodja, Ahmed Bader, Assia Benabdallah (1999)

ESAIM: Control, Optimisation and Calculus of Variations

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Stabilization of second order evolution equations by a class of unbounded feedbacks

Kais Ammari, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.

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

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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...

New classes of analytic and Gevrey semigroups and applications

Angelo Favini, Roberto Triggiani (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We consider the operator $- A + i B$ on a complex Hilbert space, where $A$ is positive self-adjoint and $B$ is self-adjoint, and where, moreover, « $B$ is comparable to $A^{α}$ , $α \geq 1$ », in a technical sense. Two applications are given.

Displaying similar documents to “How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance”

The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation

On the L p -stabilization of the double integrator subject to input saturation

Dynamic stabilization of systems via decoupling techniques

Stabilization of second order evolution equations by a class of unbounded feedbacks

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

New classes of analytic and Gevrey semigroups and applications

On the $L^{p}$ -stabilization of the double integrator subject to input saturation