Frequency Weighted Model Reduction Research Articles

Frequency-weighted model reduction via quasi-Kalman decomposition

A frequency-weighted model reduction method based on quasi-Kalman decomposition is proposed for discrete systems. The method is essentially an extension of the technique presented by Lu and Lee (1985) to the frequency weighted case and can handle both single-sided as well as double-sided weights. Two illustrative examples show the effectiveness of the method and results are compared with the method developed by Enns (1984).

A new frequency-weighted balanced truncation method and an error bound

In this paper, a new frequency-weighted model reduction method with an a priori error bound is proposed. The method is a generalization of Enns' technique (1984) and yields stable models even when both input and output weightings are included. The proposed method is compared with other existing methods using numerical examples.

Discrete‐time frequency weighted model reduction and application to sampled‐data models

The problem of frequency weighted optimal model order reduction for discrete-time systems is considered. Necessary conditions which completely characterize the reduced-order model are given. The solution of the problem consists of a set of one generalized Riccati equation and two generalized Lyapunov equations all coupled by a projection. The results that were obtained for this problem are used to solve the problem of finding the optimal, fixed-order, discrete-time model for a sampled-data continuous-time system. Several configurations and cost functions, each corresponding to a certain physical scenario, are considered. Copyright © 1998 John Wiley & Sons, Ltd.

Discrete-time frequency weighted model reduction and application to sampled-data models

The problem of frequency weighted optimal model order reduction for discrete-time systems is considered. Necessary conditions which completely characterize the reduced-order model are given. The solution of the problem consists of a set of one generalized Riccati equation and two generalized Lyapunov equations all coupled by a projection. The results that were obtained for this problem are used to solve the problem of finding the optimal, fixed-order, discrete-time model for a sampled-data continuous-time system. Several configurations and cost functions, each corresponding to a certain physical scenario, are considered. Copyright © 1998 John Wiley & Sons, Ltd.

Controller approximation: approaches for preserving H/sub ∞/ performance

Investigates the design of reduced-order controllers using an H/sub /spl infin// framework. Given a stabilizing controller which satisfies a prespecified level of closed-loop H/sub /spl infin// performance, sufficient conditions are derived for another controller to be stabilizing and satisfy the same level of H/sub /spl infin//, performance. Such controllers are said to be (P,/spl gamma/)-admissible, where P is the model of the plant under consideration and /spl gamma/ is the required level of prespecified H/sub /spl infin// performance. The conditions are expressed as norm bounds on particular frequency-weighted errors, where the weights are selected to make a specific transfer function a contraction. The design of reduced-order (P,/spl gamma/)-admissible controllers is then formulated as a frequency-weighted model reduction problem. It is advantageous for the required weights to be large in some sense. Solutions which minimize either the trace, or the determinant, of the inverse weights are characterized. We show that the procedure for minimizing the determinant of the inverse weights always gives a direction where the weights are the best possible. To conclude, we demonstrate by way of a numerical example, that when used in conjunction with a combined model reduction/convex optimization scheme, the proposed design procedures are effective in substantially reducing controller complexity.

A Gradient Flow Approach To Frequency Weighted Model Reduction

In this paper, a frequency weighted model reduction technique based on optimization is presented. The cost function minimized is the impulse energy of the overall system with weights. The paper proposes to find an optimization solution by solving ordinary differential equations which are a gradient flow associated with the cost function. An example is presented to illustrate the method and is compared with Enns' method of frequency weighted model reduction.

Model reduction via directional interpolation

In this paper, we provide a model reduction method for stable MIMO linear discrete-time systems such that the reduced-order model interpolates a finite series of 1st-order information (information associated with the transfer function) and 2nd-order information (information associated with the power spectrum function) of the original system with respect to a direction. The directional interpolation approach to the model reduction guarantees the stability of the reduced-order model and can suppress the unnecessary increase of its order involved by the increase of interpolated information. We also propose an algorithm of the output frequency-weighted model reduction as an effective application of the model reduction via directional interpolation.

Frequency-weighted model reduction with [formula omitted]∞ error bounds

This paper considers frequency-weighted model reduction. The explicit lower and upper approximation error bounds are derived for certain classes of weighted model reduction problems. The approximation is based on some unweighted approximations and the error bounds are given in terms of the Hankel singular values of the weighted model.

A structured approximation problem with applications to frequency weighted model reduction

The authors consider the problem of finding necessary and sufficient conditions for the existence of a Q with no more than k poles in the closed left-half plane such that the norm of a certain matrix >

Frequency weighted model reduction via optimal projection

The problem of order reduction with frequency weighting is considered. Necessary conditions characterizing the reduced-order model which minimizes a quadratic error criterion in the frequency domain, with either input or output frequency weighting, are given. The problem is transformed to the time domain where the weighting matrix is expressed as a shaping filter that generates colored noise at the input. When the weighting matrix is singular at infinity, the reduced-order model has a direct transmission term even if the original system is strictly proper. This additional degree of freedom can be used to obtain better approximation over a prespecified frequency range.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>