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Finite Element Approximation of Lyapunov Equations Related to Parabolic Stochastic PDEs. [PDF]

Appl Math Optim
Andersson A, Lang A, Petersson A, Schroer L.   +3 more
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On the Lyapunov matrix differential equation

IEEE Transactions on Automatic Control, 1986
A lower bound for the determinant of the solution to the Lyapunov matrix differential equation is derived. It is shown that this bound is obtained as a solution to a simple scalar differential equation. In the limiting case where the solution to the Lyapunov differential equation becomes stationary, the result reduces to one of the existing bounds for ...
Mori, Takehiro, Fukuma, Norio, Kuwahara, Michiyoshi   +2 more
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Solving the Matrix Differential Riccati Equation: A Lyapunov Equation Approach

IEEE Transactions on Automatic Control, 2010
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Nguyen, Thang, Gajic, Zoran
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Bounds in the Lyapunov matrix differential equation

IEEE Transactions on Automatic Control, 1987
Upper and lower bounds for the trace of the solution of the Lyapunov matrix differential equation are derived. It is shown that they are obtained as solutions to simple scalar differential equations. As a special case, the bounds for the stationary solution give ones for the solution to the Lyapunov algebraic equation.
Mori, T., Fukuma, N., Kuwahara, M.
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A numerical approach based on Bernstein collocation method: Application to differential Lyapunov and Sylvester matrix equations

Mathematics and Computers in Simulation, 2023
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Lakhlifa Sadek, Ahmad Sami Bataineh, Osman Rasit Isik, Hamad Talibi Alaoui, Ishak Hashim   +4 more
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Solving the singularly perturbed matrix differential Riccati equation: A Lyapunov equation approach

Proceedings of the 2010 American Control Conference, 2010
In this paper, we study the finite time (horizon) optimal control problem for singularly perturbed systems. The solution is obtained in terms of the corresponding solution of the algebraic Riccati equation and the decomposition of the singularly perturbed differential Lyapunov equation into reduced-order differential Lyapunov/Sylvester equations.
null Thang Nguyen, Zoran Gajic
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Stability and the matrix Lyapunov equation for delay differential systems

International Journal of Control, 1989
Abstract Asymptotic stability independent of the delay of linear differential delay systems with commensurate and non-commensurate delays is analysed using 2-D (two-dimensional) and n-D (n-dimensional) state-space models. Sufficient conditions for stability are obtained in terms of the frequency dependent 1-D (one-dimensional) Lyapunov equations.
P. Agathoklis, S. Foda
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Upper and lower bounds for the solution of the Lyapunov matrix differential equation

Linear and Multilinear Algebra
Jianzhou Liu, Ze Zhang, Wenlong Zeng, Fuying Tang   +3 more
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Lyapunov-type functions and invariant sets for Riccati matrix differential equations

1997 European Control Conference (ECC), 1997
We present two different methods to obtain global existence results for solutions of nonsymmetric Riccati matrix differential equations. In the first approach we derive sufficient conditions ensuring that the spectral norm of the solutions remains uniformly bounded in an interval (−∞, to]: in a second part we make use of the linearizability of the ...
G. Freiling, G. Jank, A. Sarychev
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