An algorithm for companion form realization

Tsui, Chia-Chi; Chen, C. T.

doi:10.1080/00207178308933110

Cited by 3 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, only the polynomial matrix fraction description (MFD) form of G(s) can be used effectively in design [1−3] , while this form of G(s) has a one-to-one parametric relation with a special canonical form (with state matrix A) of state space model [1,4,5] . The numbers of unknown parameters of state matrices A and A are n × n and only (m or p) ×n, respectively.…”

Section: System and Observer Definitionsmentioning

confidence: 99%

Observer design — A survey

Tsui

2015

Int. J. Autom. Comput.

View full text Add to dashboard Cite

This paper surveys the results of observer design for linear time-invariant (L-T-I) deterministic irreducible open-loop systems (OLS), the most basic type of OLS. An observer estimates Kx x x(t) signal where K is a constant and x x x(t) is the state vector of the OLS. Thus, an observer can be used as a feedback controller that implements state feedback control (SFC) or Kx x x(t)-control, and observer design is therefore utterly important in all feedback control designs of state space theory. In this survey, the observer design results are divided into three categories and for three respective main purposes. The first category of observers estimate signal Kx x x(t) only with a given K, and this survey has four conclusions: 1) Function observer that estimates Kx x x(t) directly is more general than state observer that estimates x x x(t), and may be designed with order lower than that of state observer, and the additional design objective is to minimize observer order; 2) The function observer design problem has already been simplified to the solving of a single set of linear equations only while seeking the lowest possible number of rows of the solution matrix, and an apparently most effective and general algorithm of solving such a problem can guarantee unified upper and lower bounds of the observer order; 3) Because such a single set of linear equations is the simplest possible theoretical formulation of the design problem and such theoretical observer order bounds are the lowest possible, and because the general, simple, and explicit theoretical formula for the function observer order itself do not exist, the theoretical part of this design problem is solved; 4) Because the function observer order is generically near its upper bound, further improvement on the computational design algorithm so that the corresponding observer order can be further reduced, is generically not worthwhile. The second category of observers further realize the loop transfer function and robustness properties of the direct SFC, and the conclusion of this survey is also fourfold: 1) To fully realize the loop transfer function of a practically designed Kx x x(t)-control, the observer must be an output feedback controller (OFC) which has zero gain to OLS input; 2) If parameter K is separately designed before the observer design, as in the separation principle which has been followed by almost all people for over half of a century, then OFC that estimates Kx x x(t) does not exist for almost all OLS s; 3) As a result, a synthesized design principle that designs an OFC first and is valid for almost all OLS s, is proposed and fully developed, the corresponding K will be designed afterwards and will be constrained by the OFC order as well as the OFC parameters; 4) Although the Kx x x(t)-control is constrained in this new design principle and is therefore called the "generalized SFC" (as compared to the existing SFC in which K is unconstrained), it is still strong enough for most OLS s and this new design principle overcomes many fund...

show abstract

Section: System and Observer Definitionsmentioning

confidence: 99%

Observer design — A survey

Tsui

2015

Int. J. Autom. Comput.

View full text Add to dashboard Cite

show abstract

Algorithm for minimal realization of linear multivariable systems

Sebakhy

Singaby²

1989

International Journal of Systems Science

View full text Add to dashboard Cite

Based on an iterative algorithm developed by the authors for computing the invariant zeros of linear systems as eigenvalues, a new algorithm for minimal realization of linear multivariable control systems is presented. This method of realization gives new insight into the problem of constructing a linear multivariable system by using its pole-zero characterization. Two numerical examples are presented to show the feasibility of the proposed method.

show abstract

An Algorithm For Minimal Realization Of Linear Multivariable Systems

Sebakhy

Singaby²

Proceedings of the 1988 IEEE International Conference on Systems, Man, and Cybernetics

View full text Add to dashboard Cite

An algorithm for companion form realization

Cited by 3 publications

References 7 publications

Observer design — A survey

Observer design — A survey

Algorithm for minimal realization of linear multivariable systems

An Algorithm For Minimal Realization Of Linear Multivariable Systems

Contact Info

Product

Resources

About