Displaying similar documents to “Ingham-type inequalities and Riesz bases of divided differences”

Boundary feedback stabilization of a three-layer sandwich beam: Riesz basis approach

Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss...

Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.

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

Birgit Jacob, Hans Zwart (2001)

International Journal of Applied Mathematics and Computer Science

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In this paper equivalent conditions for exact observability of diagonal systems with a one-dimensional output operator are given. One of these equivalent conditions is the conjecture of Russell and Weiss (1994). The other conditions are given in terms of the eigenvalues and the Fourier coefficients of the system data.

Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.