# On suboptimal linear system reduction

01 Nov 1975-Vol. 63, Iss: 11, pp 1610-1611

...read more

##### Citations

More filters

••

[...]

TL;DR: Topics such as stability theory, linear prediction, and parameter identification, system synthesis and implementation, two-dimensional filtering, decentralized control and estimation, and image processing are examined in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the two disciplines.

Abstract: The purpose of this paper is to explore several current research directions in the fields of digital signal processing and modern control and estimation theory. We examine topics such as stability theory, linear prediction, and parameter identification, system synthesis and implementation, two-dimensional filtering, decentralized control and estimation, and image processing, in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the two disciplines.

70 citations

••

[...]

TL;DR: A simplified approach for model order reduction (MOR) idea is planned for better understanding and explanation of largescale linear dynamical (LSLD) system, which proves to be an excellent match as compared to the response obtained by other methods in the literature review with the original system.

Abstract: A simplified approach for model order reduction (MOR) idea is planned for better understanding and explanation of largescale linear dynamical (LSLD) system. Such approaches are designed to well understand the description of the LSLD system based upon the Balanced Singular Perturbation Approximation (BSPA) approach. BSPA is tested for minimum / non-minimal and continuous/discrete-time systems valid for linear time-invariant (LTI) systems. The reduced-order model (ROM) is designed to preserved complete parameters with reasonable accuracy employing MOR. The Proposed approach is based upon retaining the dominant modes (may desirable states) of the system and eliminating comparatively the less significant eigenvalues. As the ROM has been derived from retaining the dominant modes of the largescale linear dynamical stable system, which preserves stability. The strong aspect of the balanced truncation (BT) method is that the steady-state values of the ROM do not match with the original system (OS). The singular perturbation approximation approach (SPA) has been used to remove this drawback. The BSPA has been efficaciously applied on a large-scale system and the outcomes obtained show the efficacy of the approach. The time and frequency response of an approximated system has been also demonstrated by the proposed approach, which proves to be an excellent match as compared to the response obtained by other methods in the literature review with the original system. KeywordsMOR, Large-scale linear dynamical system, Balanced truncation method, Steady state value, Singular perturbation approximation.

2 citations

### Cites methods from "On suboptimal linear system reducti..."

[...]

[...]

••

[...]

TL;DR: In this paper, a modified balanced truncation method (BTM) was proposed to adjust the steady-state value of the response transfer matrix of the reduced-order model (ROM) without affecting the variations in dynamical behaviour as compared to the original system.

Abstract: Most of the physical structures may be described in terms of mathematical models. The mathematical methods of system modelling also lead to a thorough explanation of the mechanism in the form of mathematical equations, which are often difficult to use for both analysis and controller synthesis. Consequently, it is useful and very important to determine the likelihood of different calculations of the same type, but in a lower-order representation, which can be assumed to correctly represent almost all the basic features of the system under examination. In this article, the proposed method is based on the modified balanced truncation method (BTM) by which the steady-state value from the problem of the BTM has been circumvented. This weakness has been eliminated by using a modified BTM to narrow the deviations by incorporating a gain factor into the response transfer matrix of the reduced-order model (ROM) to adjust the steady-state value of the ROM, without affecting the variations in dynamical behaviour as compared to the original system. To illustrate the proposed method, a real-time application model has been reduced where the ROM retains all the essential characteristics of the original system. In order to analyse the effectiveness, accuracy and validation with the other existing reduction methods, two standard numerical test systems have been taken from the literature and been tested also.

1 citations

••

[...]

01 Jan 1984

TL;DR: The object of the present paper is to point out the application of state-space models in comparatively less known areas such as sequential machines and computers, and the extension of one-dimensional models to multidimensional ones.

Abstract: Considerable interest has been shown recently in the mathematical modelling of linear systems. A number of investigators considered the reduction of these models into equivalent reduced ordered models. The object of the present paper is to point out the application of state-space models in comparatively less known areas such as sequential machines and computers, and the extension of one-dimensional models to multidimensional ones. Petri-Net approach is considered a good tool for handling problems of parallel processings and concurrency. Petri Nets can also conveniently be represented in the state equation form. Several results obtained by the author and his co-workers in the areas of one and two-dimensional systems, sequential machines and mathematical modelling using Petri Nets are reviewed. The use of three-dimensional models in the promissing area of robotics are discussed.

##### References

More filters

[...]

01 Jan 1965

TL;DR: Markov parametric algorithm for effective construction of minimal realizations of linear state-variable finite-dimensional dynamical systems from input-output data is presented in this article, where a Markov-parametric algorithm is used to construct the minimal realization.

Abstract: Markov parametric algorithm for effective construction of minimal realizations of linear state-variable finite-dimensional dynamical systems from input-output data

908 citations

••

[...]

TL;DR: Realization theory for both time-invariant and time-variable linear systems is developed and its applicability to linear quadratic control and filtering is discussed in this paper, where the emphasis is on obtaining physically meaningful realizations and several procedures which accomplish this are detailed.

Abstract: Realization theory for both time-invariant and time-variable linear systems is developed and its applicability to linear quadratic control and filtering is discussed. For time-invariant systems a review of canonical structure theory is given and various properties such as minimality and equivalence are characterized in terms of the Hankel matrix. Realization theory for such systems is then developed based on the Hankel matrix and a new computational algorithm is presented. For time-variable systems the emphasis is on obtaining physically meaningful realizations and several procedures which accomplish this are detailed. For "constant rank" systems, a generalization of the Hankel matrix approach is also presented.

250 citations

[...]

01 Jan 1973

TL;DR: A variant of the Ho's Algorithm that generates approximate realizations of specified dimension from approximate data is discussed.

213 citations

••

[...]

TL;DR: In this article, a variant of Ho's algorithm that generates approximate realizations of specified dimension from approximate data is discussed. But it is not shown how to apply it to the problem of finite-dimensional linear systems.

Abstract: Ho's Algorithm generates exact realizations of finite-dimensional linear systems, given exact data. We discuss here a variant of the algorithm that generates approximate realizations of specified dimension from approximate data.

211 citations

••

[...]

TL;DR: In this article, an algorithm for constructing minimal linear finite-dimensional realizations (a minimal partial realization) of an unknown (possibly infinite-dimensional) system from an external description as given by its Markov parameters is presented.

Abstract: An algorithm for constructing minimal linear finite-dimensional realizations (a minimal partial realization) of an unknown (possibly infinite-dimensional) system from an external description as given by its Markov parameters is presented. It is shown that the resulting realization in essence models the transient response of the unknown system. If the unknown system is linear, this technique can be used to find a smaller dimensional linear system having the same transient characteristics. If the unknown system is nonlinear, the technique can be used either 1) to determine a useful nonlinear model, or 2) te determine a linear model, both of which approximate the transient response of the nonlinear system.

152 citations

##### Related Papers (5)

[...]

[...]

[...]