Showing papers by "Takehiro Mori published in 1986"
TL;DR: In this article, an explicit solution to the algebraic Lyapunov matrix equation is obtained in terms of the controllability matrix of the pair of coefficient matrices, which enables us to determine the number of positive eigenvalues of the positive semidefinite solution through the covariance matrix.
Abstract: An explicit solution to the algebraic Lyapunov matrix equation is obtained in terms of the controllability matrix of the pair of coefficient matrices. This enables us to determine the number of positive eigenvalues of the positive semidefinite solution through the controllability matrix. Based on this explicit formula, upper and lower bounds for each eigenvalue of the solution are derived, which always give nontrivial estimates.
39 citations
TL;DR: A lower bound for the determinant of the solution to the Lyapunov matrix differential equation is derived and it is shown that this bound is obtained as a solution to a simple scalar differential equation.
Abstract: 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 the algebraic equation.
16 citations
TL;DR: In this article, a simple sufficient stability criterion for linear discrete systems with parameter-variation was proved to be necessary and sufficient for the stability of a class of such systems with parameters.
Abstract: A simple sufficient stability criterion for linear discrete systems obtained previously is proved to be necessary and sufficient for the stability of a class of such systems with parameter-variation.
12 citations
TL;DR: In this article, the stability condition for linear discrete systems was extended to cover time-varying systems, and it was pointed out that the condition can be naturally extended to include time varying systems.
Abstract: Some additional comments are offered on the stability condition for linear discrete systems in Dabke (1983). It is pointed out that the condition can be naturally extended to cover time-varying systems.
2 citations
01 Dec 1986
TL;DR: Several stability and instatility criteria are provided for linear time-delay systems and a part of the results is a generalization of the formerly reported stability theorems and other part forms an instability counterpart of them.
Abstract: Several stability and instatility criteria are provided for linear time-delay systems. A part of the results is a generalization of the formerly reported stability theorems and other part forms an instability counterpart of them. Stability or instability property of the systems is checked by examining whether the eigenvalue-loci of some matrix involving system parameters lie in certain region of the complex plane. This task can be successfully carried out with the aid of personal computers with graphic display terminals. Some examples are worked out to demonstrate the present approach.
2 citations
2 citations