• 전자공학회논문지 IE
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• v.44 no.4
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• pp.26-29
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• 2007

In this paper, we use Lyapunov equations and functions to consider the linear systems with perturbed system matrices. And we consider that what choice of Lyapunov function V would allow the largest perturbation and still guarantee that V is negative definite. We find that this is determined by testing for the existence of solutions to a related quadratic equation with matrix coefficients and unknowns the matrix Riccati equation.

• International Journal of Control, Automation, and Systems
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• v.1 no.4
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• pp.459-463
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• 2003

In this paper, new results using bounds for the solution of the discrete Lyapunov matrix equation are proposed, and some of the existing works are generalized. The bounds obtained are advantageous in that they provide nontrivial upper bounds even when some existing results yield trivial ones.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.443-445
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• 1998

In this paper, an alternate method for state-covariance assignment for SISO(single input single output) linear systems is proposed. This method is based on the inverse solution of the Lyapunov matrix equation and the resulting formulas are similar in structure to the formulas for pole placement. Further, the set of all assignable covariance matrices to a SISO linear system is also characterized.

• Journal of the Korean Institute of Telematics and Electronics
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• v.16 no.5
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• pp.18-26
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• 1979

This paper extends some well-known system theories on algebraic matrix Lyapunov and Riccati equations. These extended results contain two point boundary conditions in matrix differential equations and include conventional results as special cases. Necessary and sufficient conditions are derived under which linear systems are stabilizable with feedback gains derived from periodic two-point boundary matrix differential equations. An iterative computation method for two-point boundary differential Riccati equations is given with an initial guess method. The results in this paper are related to periodic feedback controls and also to the quadratic cost problem with a discrete state penalty.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.2
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• pp.78-82
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• 1995

In this paper, we consider the robustness analysis problem in state space models with linear time invariant perturbations. Based upon the discrete-time Lyapunov approach, sufficient conditions are derived for the eigenvalues of perturbed matrix to be located in a circle, and robustness bounds on perturbations are obtained. Spaecially, for the case of a diagonalizable hermitian matrix the bound is given in terms of the nominal matrix without the solution of Lyapunov equation. This robustness analysis takes account not only of stability robustness but also of certain types of performance robustness. For two perturbation classes resulting bounds are shown to be improved over the existing ones. Examples given include comparison of the proposed analysis method with existing one.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.807-816
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• 2014

The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.288-294
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• 2008

Motivated by the fact that upper solution bounds for the continuous Lyapunov equation are valid under some very restrictive conditions, an attempt is made to extend the set of Hurwitz matrices for which such bounds are applicable. It is shown that the matrix set for which solution bounds are available is only a subset of another stable matrices set. This helps to loosen the validity restriction. The new bounds are illustrated by examples.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.1
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• pp.34-42
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• 2009

In this paper, new bounds for the solution of the unified Lyapunov matrix equation for decentralized singularly perturbed systemare obtained, and some of the existing works using deficient assumptions are also generalized.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.485-486
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• 2007

In this paper, we use Lyapunov equations and functions to consider the linear systems with perturbed system matrices. And we consider that what choice of Lyapunov function V would allow the largest perturbation and still guarantee that V is negative definite. We find that this is determined by testing for the existence of solutions to a related quadratic equation with matrix coefficients and unknowns the so-called matrix Riccati equation.

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.501-508
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• 2004

A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N-th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed for a discrete state delay system whose state delay is not exactly known but only known to lie in a certain interval.