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Approximation and model order reduction for second order systems with Levy-noise
1. | Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany, Germany |
References:
[1] |
A. C. Antoulas, Approximation of large-scale dynamical systems,, Advances in Design and Control 6. Philadelphia, (2005). |
[2] |
P. Benner and T. Damm, Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems,, SIAM J. Control Optim., 49 (2011), 686. |
[3] |
R. F. Curtain, Stability of Stochastic Partial Differential Equation,, J. Math. Anal. Appl., 79 (1981), 352. |
[4] |
T. Damm, Rational Matrix Equations in Stochastic Control,, Lecture Notes in Control and Information Sciences 297, (2004). |
[5] |
W. Grecksch and P. E. Kloeden, Time-discretised Galerkin approximations of parabolic stochastic PDEs,, Bull. Aust. Math. Soc., 54 (1996), 79. |
[6] |
E. Hausenblas, Approximation for Semilinear Stochastic Evolution Equations,, Potential Anal., 18 (2003), 141. |
[7] |
A. Jentzen and P. E. Kloeden, Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise,, Proc. R. Soc. A 2009, 465 (2009), 649. |
[8] |
B. C. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction,, IEEE Trans. Autom. Control, 26 (1981), 17. |
[9] |
S. Peszat and J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise. An evolution equation approach,, Encyclopedia of Mathematics and Its Applications 113, (2007). |
[10] |
A. J. Pritchard and J. Zabczyk, Stability and Stabilizability of Infinite-Dimensional Systems,, SIAM Rev., 23 (1981), 25. |
[11] |
M. Redmann and P. Benner, Model Reduction for Stochastic Systems,, Stoch PDE: Anal Comp, 3(3) (2015), 291. |
show all references
References:
[1] |
A. C. Antoulas, Approximation of large-scale dynamical systems,, Advances in Design and Control 6. Philadelphia, (2005). |
[2] |
P. Benner and T. Damm, Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems,, SIAM J. Control Optim., 49 (2011), 686. |
[3] |
R. F. Curtain, Stability of Stochastic Partial Differential Equation,, J. Math. Anal. Appl., 79 (1981), 352. |
[4] |
T. Damm, Rational Matrix Equations in Stochastic Control,, Lecture Notes in Control and Information Sciences 297, (2004). |
[5] |
W. Grecksch and P. E. Kloeden, Time-discretised Galerkin approximations of parabolic stochastic PDEs,, Bull. Aust. Math. Soc., 54 (1996), 79. |
[6] |
E. Hausenblas, Approximation for Semilinear Stochastic Evolution Equations,, Potential Anal., 18 (2003), 141. |
[7] |
A. Jentzen and P. E. Kloeden, Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise,, Proc. R. Soc. A 2009, 465 (2009), 649. |
[8] |
B. C. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction,, IEEE Trans. Autom. Control, 26 (1981), 17. |
[9] |
S. Peszat and J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise. An evolution equation approach,, Encyclopedia of Mathematics and Its Applications 113, (2007). |
[10] |
A. J. Pritchard and J. Zabczyk, Stability and Stabilizability of Infinite-Dimensional Systems,, SIAM Rev., 23 (1981), 25. |
[11] |
M. Redmann and P. Benner, Model Reduction for Stochastic Systems,, Stoch PDE: Anal Comp, 3(3) (2015), 291. |
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