• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.4 no.1
• /
• pp.1-6
• /
• 2004

This paper deals with a balanced model reduction for T-S(Takagi-Sugeno) fuzzy systems with time varying state delay. We define a generalized controllability gramian and a generalized observability gramian for a stable T-S fuzzy delayed systems. We obtain a balanced state space realization using the generalized controllability and observability gramian and obtain a reduced model by truncating states from the balanced state space realization. We also present an upper bound of the approximation error. The generalized controllability gramian and observability gramian can be computed from solutions of linear matrix inequalities. We demonstrate the efficacy of the suggested method by illustrating a numerical example.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.16 no.2
• /
• pp.144-149
• /
• 2006

This paper deals with a balanced model reduction for uncertain nonlinear systems via T-S fuzzy approach. We define a generalized controllability/observability gramian and obtain a balanced state space model using generalized gramians which can be obtained from solutions of linear matrix inequalities. We present a balanced model reduction scheme by truncating not only state variables but also uncertain elements. An upper bound of the model reduction error will also be suggested. In order to demonstrate the efficacy of our method, a numerical example will be presented.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.13 no.6
• /
• pp.510-520
• /
• 1988

In this paper, the output error variance due to the differential vcariation of the state-space coefficient [ABCD], which is the coefficient quentization error, is normalized on the variance for cases that infinite wordlength state-space digital filter is realized by the finite one. That is, defining S as the statistical sensitivity and extending controllability gramian, observability gramian, and 2nd order mode analysis method to the state space digital filter, we synthesize the realization structure with the minimum statistical sensitivity and prove the effecency of the minimum statistical sensitivity structure synthesis by the simulation.

• Journal of Institute of Control, Robotics and Systems
• /
• v.8 no.5
• /
• pp.351-356
• /
• 2002

This papaer deals with a model reduction problem for linear systems with time varying parameters. For this problem, a controllability Grammian and an observability Grammian are introduced and computed by solving linear matrix inequalities. Using the controllability/observability Grammian, a balanced state space realization for linear parameter varying systems is obtained. From the balanced state space realization, a reduced model can be obtained by truncating not only states but also time varying parameters and an upper bound of the model reduction error is derived as well.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.17 no.9
• /
• pp.909-917
• /
• 1992

This paper proposes the realization of state-space digital filters with minimum output error variance. The algorithm is transforms of controllability and observability gramian in linear time invariant systems by weighted function and can improve performance of the digital filters by reducing the put error variance for state space coeffient variation. A numerical example shows that algorithm structure has much lower output error variance than that of other four structures(canonical, parallel, statistical sensitivity, balanced).

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10a
• /
• pp.1219-1219
• /
• 1991

This paper proposes the model order reduction with pass band error reduction in the frequency domain of discrete time linear systems. The algorithm is the new method of reduced order model which reduces passband error by changing controllability and observability gramian used with weighted functions. A numerical example shows that this algorithm has lower passband error than balanced w&l and weighted function characteristics in frequency domain.

• 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.