Model Reduction Of Discrete-time Systems Research Articles

Model reduction of discrete-time systems in limited intervals

Model order reduction (MOR) is a process of obtaining a lower order surrogate model that accurately approximates the original high-order system. Since no actuator or plant operates over the entire time and frequency ranges, the reduced-order model should be accurate in the actual range of operation. In this paper, model reduction techniques for discrete time systems are presented that ensure less reduction error in the specified time and frequency intervals. The techniques are tested on the benchmark numerical examples and their efficacy is shown.

Partial fraction expansion based frequency weighted model reduction for discrete-time systems

In this paper, a partial fraction expansion based frequency weighted model reduction algorithm is developed for discrete-time systems. The proposed method is an extension to the method by Sreeram et al. [13] and it yields stable reduced order models with both single and double sided weighting functions. Effectiveness of the proposed algorithm is demonstrated by a numerical example.

Parallel algorithms for model reduction of discrete-time systems

Computing reduced-order models of controlled dynamical systems is of fundamental importance in many analysis and synthesis problems in systems and control theory. Algorithmic aspects of model reduction methods based on state-space truncation for linear discrete-time systems are addressed here. In contrast to the often-used approach of applying methods for continuous-time systems to discrete-time models employing a bilinear transformation, we devise special algorithms for discrete-time systems. Usually, this is more reliable and efficient. All methods discussed require in an initial stage the computation of the Gramians of the system. Using an accelerated fixed-point iteration for computing the full-rank factors of the Gramians yields some favorable computational aspects, particularly for non-minimal systems. The computations only require efficient implementations of basic linear algebra operations readily available on modern computer architectures. We discuss aspects of the parallel implementation of these methods and show the performance and scalability on distributed memory computers. Our approach enables users to deal with very complex systems using relatively cheap infrastructure, as, for example, a local PC or workstation network.

A new approach for frequency weightedL2 model reduction of discrete-time systems

This paper deals with the problem of model reduction based on an optimization technique. The objective function being minimized in the impulse energy of the overall system with unity, single-sided and double-sided weightings. A number of properties of the gradient flows associated with the objective function are obtained. Two examples are presented to illustrate the effectiveness of the proposed method, and results are compared with unweighted and weighted balanced truncation methods. © 1998 John Wiley & Sons, Ltd.

Quasi-optimal model reduction of discrete-time systems

A novel noniterative method is presented for deriving reduced-order models of linear discrete-time systems without solving any nonlinear equation. The resulting error energy is usually relatively close to optimal.

A second multivariable normal form for model reduction of discrete-time systems

Starting by the block-controllability form, a normal form for multivariable discrete-time systems is developed. The construction of this normal form is made straight-forward by the introduction of the matrix Schur-Cohn table. It shows a one-to-one (scalar-to-matrix) correspondence with the single-input Mansour form [2]. Examples for the construction of the proposed form as well as its application to model reduction are also given.

A multivariable normal-form for model reduction of discrete-time systems

The normal form derived by Mansour [I] for single-input/single-output, time-invariant, linear discrete systems will be extended to the multivariable case. An algorithm will be used to achieve simple computation of this form starting with the Luenberger first canonical form. The construction of this form will be illustrated by examples applied to model reduction of multivariable discrete-time systems.

Model reduction of discrete-time systems using the schwarz canonical form

The Schwarz canonical form description of a linear discrete-time system will be used to derive reduced-order models which are stable if the original system is stable. Further, the steady-state response of the models to a step input is equal to that of the system.