D-decomposition technique state-of-the-art

Gryazina, Elena; Polyak, B. T.; Tremba, Andrey

doi:10.1134/s0005117908120011

Cited by 92 publications

(45 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We apply the D decomposition method of Nejmark (see [23] for the state of the art and [10] as an example of application) for determining the stability region of (4) in the complex…”

Section: The Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Stability conditions for linear continuous-time fractional-order state-delayed systems

Busłowicz

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

Abstract. The stability problem of continuous-time linear fractional order systems with state delay is considered. New simple necessary and sufficient conditions for the asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix and time delay. It is shown that in the complex plane there exists such a region that location in this region of all eigenvalues of the state matrix multiplied by delay in power equal to the fractional order is necessary and sufficient for the asymptotic stability. Parametric description of boundary of this region is derived and simple new analytic necessary and sufficient conditions for the stability are given. Moreover, it is shown that the stability of the fractional order system without delay is necessary for the stability of this system with delay. The considerations are illustrated by a numerical example.

show abstract

“…We apply the D decomposition method of Nejmark (see [23] for the state of the art and [10] as an example of application) for determining the stability region of (4) in the complex…”

Section: The Main Resultsmentioning

confidence: 99%

“…The stability problem of standard (i.e. non-fractional) continuoustime linear systems with pure delay has been considered in [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Stability conditions for linear continuous-time fractional-order state-delayed systems

Busłowicz

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

show abstract

“…Also, matrix A + BKC is stable if all eigenvalues are in the open left-half plane for a continuous-time system and all eigenvalues are in the open unit disc for a discrete-time system; see [6]. Furthermore, assume that matrix A does not have zero or imaginary eigenvalues for the continuous-time subsystem (2) and does not have eigenvalues on the unit circumference for the discrete one (3).…”

Section: D-decomposition Theory With Periodic Sampling Of Lth Ordermentioning

confidence: 99%

“…There exist less number of stability results for nonuniform sampling than for uniform sampling. This work investigates the problem of the stability of a non-uniformly sampled system with the use of the D-decomposition method; see, for example, [6,7]. The idea of D-decomposition is based on determining the regions on a parameter plane obtained from a characteristic equation with simple parametrization by jω.…”

Section: Introductionmentioning

confidence: 99%

On D-decomposition of periodically sampled systems

Janczak

2017

automat

View full text Add to dashboard Cite

The problem of the stability of non-uniformly sampled systems is considered. For this purpose, the D-decomposition method for determining the stability region in parameter space is investigated. Moreover, basic information about non-uniform sampling are presented, with an emphasis on periodic sampling. Based on the obtained simulation results, some comparisons of systems with different sampling patterns are considered.

show abstract

“…Nowadays, the D-decomposition technique is usually used together with mathematical models to find the gains of linear and H ∞ controllers [21][22][23][24][25]. However, few works in the literature apply the D-decomposition technique to find the stabilising gains from measured FRFs.…”

Section: Introductionmentioning

confidence: 99%

PD controller synthesis from open-loop response measurements of rotating system

Buttini

Nicoletti

2012

IET Control Theory Appl.

View full text Add to dashboard Cite

Abstract:In this work, a method of computing PD stabilising gains for rotating systems is presented based on the D-decomposition technique, which requires the sole knowledge of frequency response functions. By applying this method to a rotating system with electromagnetic actuators, it is demonstrated that the stability boundary locus in the plane of feedback gains can be easily plotted, and the most suitable gains can be found to minimise the resonant peak of the system. Experimental results for a Laval rotor show the feasibility of not only controlling lateral shaft vibration and assuring stability, but also helps in predicting the final vibration level achieved by the closed-loop system. These results are obtained based solely on the input-output response information of the system as a whole.

show abstract

D-decomposition technique state-of-the-art

Cited by 92 publications

References 45 publications

Stability conditions for linear continuous-time fractional-order state-delayed systems

Stability conditions for linear continuous-time fractional-order state-delayed systems

On D-decomposition of periodically sampled systems

PD controller synthesis from open-loop response measurements of rotating system

Contact Info

Product

Resources

About