Related papers: Controllability and observability for non-autonomo…
In this paper, we investigate the Hautus test for evolution equation with the operators depending on time.
We analyze the averaged controllability properties of random evolution Partial Differential Equations. We mainly consider heat and Schr\"odinger equations with random parameters, although the problem is also formulated in an abstract frame.…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
It is classical that uniform stabilization of solutions to the autonomous damped wave equation is equivalent to every geodesic meeting the positive set of the damping, which is called the geometric control condition. In this paper, it is…
We discuss the observability of a one-dimensional Schr\"odinger equation on certain time dependent domain. In linear moving case, we give the exact boundary and pointwise internal observability for arbitrary time. For the general moving, we…
In this article, we study the observability (or, equivalently, the controllability) of some subelliptic evolution equations depending on their step. This sheds light on the speed of propagation of these equations, notably in the…
In this paper we investigate a class of nonautonomous linear parabolic problems with time depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper…
We provide general product formulas for the solutions of non-autonomous abstract Cauchy problems. The main technical tool is the application of evolution semigroup methods, allowing the direct application of existing results on autonomous…
We analyse stability of observability estimates for solutions to wave and Scr\" odinger equations subjected to additive perturbations. The paper generalises the recent averaged observability/control result by allowing for systems consisting…
We study solutions to the Cauchy problem for the linear and nonlinear Schroedinger equation with a quadratic Hamiltonian depending on time. For the linear case the evolution operator can be expressed as an integral operator with the…
The problem of partial null controllability for linear autonomous evolution equations, which are controlled by a one-dimensional control, is under consideration. The partial null-controllability conditions for coupled abstract evolution…
In this paper, we build up two observability inequalities from measurable sets in time for some evolution equations in Hilbert spaces from two different settings. The equation reads: $u'=Au,\; t>0$, and the observation operator is denoted…
We consider evolution equations of the form \begin{equation*}\label{Abstract equation} \dot u(t)+ A(t)u(t)=0,\ \ t\in[0,T],\ \ u(0)=u_0, \end{equation*} where $A(t),\ t\in [0,T],$ are associated with a non-autonomous sesquilinear form…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
We characterize the observability property (and, by duality, the controllability and the stabilization) of the wave equation on a Riemannian manifold $\Omega,$ with or without boundary, where the observation (or control) domain is…
In this paper we consider second order evolution equations with unbounded dynamic feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We…
In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.
This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss the approximate controllability of…