We introduce a model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional rod. We actually consider the anisotropic elastodynamic system in the n-dimensional body and the Euler-Bernouilli beam in the one-dimensional rod. These equations are coupled via their boundaries. Using appropriate feedbacks on a part of the boundary we show the exponential decay of the energy of the system.

We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary control...

Let $L$ be a parabolic second order differential operator on the domain $\overline{\Pi }=\left[0,T\right]\times ℝ.$ Given a function $\widehat{u}:ℝ\to R$ and $\widehat{x}\>0$ such that the support of $\widehat{u}$ is contained in $(-\infty ,-\widehat{x}]$, we let $\widehat{y}:\overline{\Pi }\to ℝ$ be the solution to the equation:$$L\widehat{y}=0,\widehat{y}{|}_{\left\{0\right\}\times ℝ}=\widehat{u}.$$Given positive bounds $0\<x_0\<x_1,$ we seek a function $u$ with support in $\left[x_0,x_1\right]$ such that the corresponding solution $y$ satisfies:$$y(t,0)=\widehat{y}(t,0)\forall t\in \left[0,T\right].$$We prove in this article that, under some regularity conditions on the coefficients of $L,$ continuous solutions are unique and dense in the sense that $\widehat{y}{|}_{[0,T]\times \left\{0\right\}}$ can be $C^0$-approximated, but an exact solution does not...

Let L be a parabolic second order differential operator on the domain $\overline{\Pi }=\left[0,T\right]\times ℝ.$ Given a function $\widehat{u}:ℝ\to R$ and $\widehat{x}>0$ such that the support of û is contained in $(-\infty ,-\widehat{x}]$, we let $\widehat{y}:\overline{\Pi }\to ℝ$ be the solution to the equation: $$L\widehat{y}=0,\widehat{y}{|}_{\left\{0\right\}\times ℝ}=\widehat{u}.$$ Given positive bounds $0<x_0<x_1,$ we seek a function u with support in $\left[x_0,x_1\right]$ such that the corresponding solution y satisfies: $$y(t,0)=\widehat{y}(t,0)\forall t\in \left[0,T\right].$$ We prove in this article that, under some regularity conditions on the coefficients of L, continuous solutions are unique and dense in the sense that $\widehat{y}{|}_{[0,T]\times \left\{0\right\}}$ can be C0-approximated, but an exact solution...

A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated...

Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under...

We define, for the trace of solution of vibrating plates equation, norms with initial conditions in no regular spaces. Then, we give the corresponding exact controllability results.

Siano $A$, $B$ sottoinsiemi convessi, chiusi e limitati di uno spazio normato $X$, con le frontiere $frA$, $frB$. Dimostriamo che $h(A,B)=h(frA,frB)$, dove $h$ è la metrica di Hausdorff tra sottoinsiemi chiusi di $X$. Studiamo inoltre la continuità e la semicontinuità superiore ed inferiore di una multifunzione di tipo «frontiera».

We analyze the problem of switching controls for control systems endowed with different actuators. The goal is to control the dynamics of the system by switching from an actuator to the other in a systematic way so that, in each instant of time, only one actuator is active. We first address a finite-dimensional model and show that, under suitable rank conditions, switching control strategies exist and can be built in a systematic way. To do this we introduce a new variational principle building...

We discuss the null boundary controllability of a linear thermo-elastic plate. The method employs a smoothing property of the system of PDEs which allows the boundary controls to be calculated directly by solving two Cauchy problems.

This paper deals with the problem of time-varying differential systems when unmodeled dynamics is present. The questions related to when unmodeled dynamics (in fact when parametrical and order errors) does not affect for problems like controllability and related ones with respect to the foreseen results for a correct modelling are investigated for a wide class of typical situations. The presented results seem to be of interest in Physics when modelling uncertainties are present. Only the linear...