Results 171 to 180 of about 2,730 (204)

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.
N Fukuma
exaly   +2 more sources

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.
Thang Nguyen, Zoran Gajić
exaly   +2 more sources

Upper and lower bounds for the solution of the Lyapunov matrix differential equation

Linear and Multilinear Algebra
Jianzhou Liu
exaly   +2 more sources

Solution of the Lyapunov matrix differential equations by the frequency method

Journal of Computer and Systems Sciences International, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D. E. Kataev, I. B. Yadykin
openaire   +1 more source

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
openaire   +1 more source

The analytic structure of periodic solutions of a Lyapunov type matrix differential equation

Differential Equations, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lapitinskij, V. N., Livinskaya, V. A.
openaire   +2 more sources

Lower Eigenvalue Bounds on Summation for the Solution of the Lyapunov Matrix Differential Equation

Asian Journal of Control, 2016
AbstractIn this paper, we offer several lower bounds on eigenvalue summation for the solution of the Lyapunov matrix differential equation applying index matrix eigenvalue inequalities and Hölder inequality. Further, we give a numerical example to illustrate the effectiveness of the derived bounds.
Zhang, Juan, Liu, Jianzhou, Huang, Hao
openaire   +2 more sources

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
openaire   +3 more sources

The existence conditions of the positive semidefinite solution for the Lyapunov matrix differential equation and improvements in its bounds

Journal of the Franklin Institute
Jianzhou Liu
exaly   +2 more sources

Stability and the matrix Lyapunov equation for differential systems with delays

[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 2005
The author establishes sufficient conditions for the stability of linear and time-variant delay differential systems including their various usual subclasses (i.e., point, distributed, and mixed point-distributed delay systems). Sufficient conditions for stability are obtained in terms of the Schur complement of operators and the frequency-domain ...
openaire   +1 more source