• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.17 no.1
• /
• pp.11-19
• /
• 1992

This paper proposes a reduced order method which reduces passband error by changing controllability and observability gramian based on weighted functions in the linear time invariant system. In the case that the 4-order model is the reduced to 3-order model in the low-pass filter, the QEI in the proposed method is improved to 6.15724 compared to 10.16464 in the balanced realization method and the sensitivity is improved to 5.45962 compared to 7.790568. The frequency property curves show that the proposed method is superior to the balanced realization method.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.40 no.5
• /
• pp.326-332
• /
• 2003

This paper deals with a model reduction for linear systems with time varying delayed states. A generalized controllability and observability gramians are defined and obtained by solving linear matrix inequalities. Using the generalized controllability and observability gramians, the balanced state space equation is realized. The reduced model can be obtained by truncating states in the balanced realization and the upper bound of model approximation error is also presented. In order to demonstrate efficacy of the suggested method, a numerical example is performed.

• Journal of the Korean Society for Precision Engineering
• /
• v.14 no.1
• /
• pp.194-204
• /
• 1997

In this paper, we consider the rational approximation of multiple input delay systems. The method of computing Hankel singular values and vectors is firstly introduced, where explicitly shows the structure of the corresponding Hankel singular vectors. Secondly, rational approximants are obtained from output nor- mal relizations, which are constructed by Hankel singular values and vectors. As a result, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pad'e approximants.