Related papers: On the controllability and Stabilization of the Be…
We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system. That is, any initial state can be driven arbitrarily close to any…
Studied here is the Kawahara equation, a fifth order Korteweg-de Vries type equation, with time-delayed internal feedback. Under suitable assumptions on the time delay coefficients we prove that solutions of this system are exponentially…
This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a…
This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…
We demonstrate that chaos can be controlled using a multiplicative exponential feedback control. All three types of unstable orbits - unstable fixed points, limit cycles and chaotic trajectories can be stabilized using this control. The…
We provide explicit time-varying feedback laws that locally stabilize the two dimensional internal controlled incompressible Navier-Stokes equations in arbitrarily small time. We also obtain quantitative rapid stabilization via stationary…
In this paper, we deal with the problem of synthesizing static output feedback controllers for stabilizing polynomial systems. Our approach jointly synthesizes a Lyapunov function and a static output feedback controller that stabilizes the…
In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is shown that, in the absence of minimal…
For nonlinear systems that are known to be globally asymptotically stabilizable, control over networks introduces a major challenge because of the asynchrony in the transmission schedule. Maintaining global asymptotic stabilization in…
This article aims at providing a unified analysis of the exponential stabilization of some abstract infinite dimensional systems undergoing an event-triggering mechanism that samples the control input. The partial differential equation is…
This paper studies the exponential stabilization of a Boussinesq system describing the two-way propagation of small amplitude gravity waves on the surface of an ideal fluid, the so-called Boussinesq system of the Korteweg-de Vries type. We…
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…
The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state…
The dynamic partial differential equation (PDE) model governing longitudinal oscillations in magnetizable piezoelectric beams exhibits exponentially stable solutions when subjected to two boundary state feedback controllers. An analytically…
This paper studies the local exact controllability and the local stabilization of the semilinear Schr\"odinger equation posed on a product of $n$ intervals ($n\ge 1$). Both internal and boundary controls are considered, and the results are…
We continue our study of the problem of mixing for a class of PDEs with very degenerate noise. As we established earlier, the uniqueness of stationary measure and its exponential stability in the dual-Lipschitz metric holds under the…
Coherent feedback is a non-measurement based, hence a back-action free, method of control for quantum systems. A typical application of this control scheme is squeezing enhancement, a purely non-classical effect in quantum optics. In this…
This paper has various goals: first, we develop a local and global well-posedness theory for the regularized Benjamin-Ono equation in the periodic setting, second, we show that the Cauchy problem for this equation (in both periodic and…
In this work we address the problem of boundary feedback stabilization for a geometrically exact shearable beam, allowing for large deflections and rotations and small strains. The corresponding mathematical model may be written in terms of…
We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to rest in finite time, the absolute value of the distributed control…