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Journal ArticleDOI

Construction of minimal linear state-variable models from finite input-output data

01 Aug 1970-IEEE Transactions on Automatic Control (IEEE)-Vol. 15, Iss: 4, pp 427-436
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.
Citations
More filters
Journal ArticleDOI
TL;DR: A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm.
Abstract: A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

2,366 citations

Journal ArticleDOI
01 Jan 1991
TL;DR: Continuous-time model-based system identification as mentioned in this paper is a well-established field in the field of control systems and is concerned with the determination of particular models for systems that are intended for a certain purpose such as control.
Abstract: System identification is a well-established field. It is concerned with the determination of particular models for systems that are intended for a certain purpose such as control. Although dynamical systems encountered in the physical world are native to the continuous-time domain, system identification has been based largely on discrete-time models for a long time in the past, ignoring certain merits of the native continuous-time models. Continuous-time-model-based system identification techniques were initiated in the middle of the last century, but were overshadowed by the overwhelming developments in discrete-time methods for some time. This was due mainly to the 'go completely digital' trend that was spurred by parallel developments in digital computers. The field of identification has now matured and several of the methods are now incorporated in the continuous time system identification (CONTSID) toolbox for use with Matlab. The paper presents a perspective of these techniques in a unified framework.

373 citations

Journal ArticleDOI
TL;DR: A unitary identification procedure for linear multivariable systems based on the direct determination of a set of invariant indexes completely describing the input-output structure of the system is described.

277 citations

Journal ArticleDOI
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.

261 citations

Journal ArticleDOI
TL;DR: An efficient algorithm for obtaining solutions is given and shown to be closely related to a well-known algorithm of Levinson and the Jury stability test, which suggests that they are fundamental in the numerical analysis of stable discrete-time linear systems.
Abstract: It is common practice to partially characterize a filter with a finite portion of its impulse response, with the objective of generating a recursive approximation. This paper discusses the use of mixed first and second information, in the form of a finite portion of the impulse response and autocorrelation sequences. The discussion encompasses a number of techniques and algorithms for this purpose. Two approximation problems are studied: an interpolation problem and a least squares problem. These are shown to be closely related. The linear systems which form the solutions to these problems are shown to be stable. An efficient algorithm for obtaining solutions is given and shown to be closely related to a well-known algorithm of Levinson and the Jury stability test. The close connection between these algorithms suggests that they are fundamental in the numerical analysis of stable discrete-time linear systems.

196 citations

References
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Journal ArticleDOI
TL;DR: In this paper, it is shown that the input/output relations determine only one part of a system, that which is completely observable and completely controllable, and methods are given for calculating irreducible realization of a given impulse-response matrix.
Abstract: There are two different ways of describing uynamicu systems: (i) bymeans of state variables and (ii) by input/output relations. The first method may be regarded as an axiornatization of Newton’s laws of mechanics and is taken to be the basic definition of a system.It is then shown (in the linear case) that the input/output relations determine only one part of a system, that which is completely observable and completely controllable. Using the theory of controllability and observability, methods are given for calculating irreducible realization of a given impulse-response matrix. In particular, an explicit procedure is given to determine the minimal number of state variables necessary to realize a given transfer-function matrix. Difficulties arising from the use of reducible realizations are discussed briefly.

1,605 citations

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

Journal ArticleDOI
TL;DR: This paper presents Markov parametric algorithm for effective construction of minimal realizations of linear state-variable finite-dimensional dynamical systems from input-output data.
Abstract: Markov parametric algorithm for effective construction of minimal realizations of linear state-variable finite-dimensional dynamical systems from input-output data

167 citations