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    Wyświetlanie 1-4 z 4
    Tytuł:
    Exact Observability of Diagonal Systems With a One-Dimensional Output Operator
    Autorzy:
    Jacob, B.
    Zwart, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/908120.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    obserwator
    równanie Lyapunova
    infinite-dimensional systems
    unbounded observation operator
    exact observability
    Hautus test
    Lyapunov equations
    Opis:
    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.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1277-1283
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The motion planning problem and exponential stabilization of a heavy chain. Part II
    Autorzy:
    Grabowski, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255394.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    infinite-dimensional control systems
    semigroups
    motion planning problem
    exponential stabilization
    spectral methods
    Riesz bases
    exact observability
    Opis:
    This is the second part of paper [8], where a model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [8] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was also shown that the exponential stability can be achieved by applying a stabilizer of the colocated-type. The proof used the method of Lyapunov functionals. In the present paper, we give other two proofs of the exponential stability, which provides an additional intrinsic insight into the exponential stabilizability mechanism. The first proof makes use of some spectral properties of the system. In the second proof, we employ some relationships between exponential stability and exact observability.
    Źródło:
    Opuscula Mathematica; 2008, 28, 4; 481-505
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Exact null controllability, complete stabilizability and continuous final observability of neutral type systems
    Autorzy:
    Rabah, R.
    Sklyar, G.
    Barkhayev, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/329801.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    exact null controllability
    complete stabilizability
    final observability
    neutral type system
    Opis:
    For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property being related to exact null controllability. We also consider the case when the feedback is not bounded. We obtain a characterization of complete stabilizability for neutral type systems. Conditions for exact null controllability of neutral type systems are discussed. By duality, we obtain a result about continuous final observability. Illustrative examples are given.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 489-499
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Inverse/observability estimates for Schroedinger equations with variable coefficients
    Autorzy:
    Triggiani, R.
    Yao, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/206775.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie Schroedingera
    Carleman estimates
    exact controllability
    inverse/observability estimates
    Riemannian manifold
    Schroedinger equation
    Opis:
    We consider a general Schroedinger equation defined on an open bounded domain [Omega is a subset of R^n] with variable coefficients in both the elliptic principal part and in the first-order terms as well. At first, no boundary conditions (B.C.) are imposed. Our main result (Theorem 3.5) is a reconstruction, or inverse, estimate for solutions w: under checkable conditions on the coefficients of the principal part, the H[sup l](Omega)-energy at time t = T, or at time t = 0, is dominated by the L[sub2](Sigma)-norms of the boundary traces [...] and w[sub t] modulo an interior lower-order term. Once homogeneous B.C. are imposed, our results yield - under a uniqueness theorem, needed to absorb the lower order term - continuous observability estimates for both the Dirichlet and Neumann case, with an arbitrarily short observability time ; hence, by duality, exact controllability results. Moreover, no artificial geometrical conditions are imposed on the controlled part of the boundary in the Neuman case. In contrast to existing literature, the first step of our method employs a Riemann geometry approach to reduce the original variable coefficient principal part problem in [Omega is a subset of R^n] to a problem on an appropriate Riemannian manifold (determined by the coefficients of the principal part), where the principal part is the Laplacian. In our second step, we employ explicit Carleman estimates at the differential level to take care of the va.riable first-order (energy level) terms. In our third step, we employ micro-local analysis yielding a sharp trace estimate to remove artificial geometrical conditions on the controlled part of the boundary in the Neumann case.
    Źródło:
    Control and Cybernetics; 1999, 28, 3; 627-664
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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