Weighted multiple interpolation and the control of perturbed semigroup systems

In this paper the controllabillity and admissibility of perturbed semigroup systems are studied, using tools from the theory of interpolation and Carleson measures. In addition, there are new results on the perturbation of Carleson measures and on the weighted interpolation of functions and their derivatives in Hardy spaces, which are of interest in their own right

Stabilization and controllability of first-order integro-differential hyperbolic equations

In the present article we study the stabilization of first-order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The proof relies on a Fredholm transformation that maps the original system into a finite-time stable target system. The controllability assumption is used to prove the invertibility of such a transformation. Finally, using the method of moments, we show in a particular case that the controllability is reduced to the criterion of Fattorini

Mini-Workshop: Wellposedness and Controllability of Evolution Equations

This mini-workshop brought together mathematicians engaged in partial differential equations, operator theory, functional analysis and harmonic analysis in order to address a number of current problems in the wellposedness and controllability of infinite-dimensional systems

Exact observability of diagonal systems with a finite-dimensional output operator

In this paper equivalent conditions for exact observability of diagonal systems with a finite-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (SIAM J. Control Opt. 32(1) (1994) 1–23). The other conditions are in terms of the eigenvalues and the Lyapunov solutions of finite-dimensional subsystem

Riesz bases of port-Hamiltonian systems

The location of the spectrum and the Riesz basis property of well-posed homogeneous infinite-dimensional linear port-Hamiltonian systems on a 1D spatial domain are studied. It is shown that the Riesz basis property is equivalent to the fact that system operator generates a strongly continuous group. Moreover, in this situation the spectrum consists of eigenvalues only, located in a strip parallel to the imaginary axis and they can decomposed into finitely many sets having each a uniform gap

Exact null controllability of abstract differential equations by finite-dimensional control and strongly minimal families of exponentials

Abstract. The exact controllability to the origin for linear evolution control equation is considered. The problem is investigated by its transformation to infinite linear moment problem of generalized exponentials. The existence of solutions of obtained moment problem is investigated for the case when exponentials of a moment problem do not constitute a Riesz basis. The exact controllability of linear control system of neutral type is considered as an example

On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback

We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability are concluded for the system. Moreover, we show that the exponential stability is independent of the location of the joint. The range of the feedback gains that guarantee the system to be exponentially stable is identified