Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 8
items per page: 25 50 75
Sort by:
Download PDF Download RIS Download Bibtex

Abstract

Abstract The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.
Go to article

Authors and Affiliations

Andrzej Ruszewski
Download PDF Download RIS Download Bibtex

Abstract

Abstract The paper considers the robust stability problem of uncertain continuous-time fractional order linear systems with pure delay in the following two cases: a) the state matrix is a linear convex combination of two known constant matrices, b) the state matrix is an interval matrix. It is shown that the system is robustly stable if and only if all the eigenvalues of the state matrix multiplied by delay in power equal to fractional order are located in the open stability region in the complex plane. Parametric description of boundary of this region is derived. In the case a) the necessary and sufficient computational condition for robust stability is established. This condition is given in terms of eigenvalue-loci of the state matrix, fractional order and time delay. In the case b) the method for determining the rectangle with sides parallel to the axes of the complex plane in which all the eigenvalues of interval matrix are located is given and the sufficient condition for robust stability is proposed. This condition is satisfied if the rectangle multiplied by delay in power equal to fractional order lie in the stability region. The considerations are illustrated by numerical examples.
Go to article

Authors and Affiliations

Mikołaj Busłowicz
Andrzej Ruszewski
Download PDF Download RIS Download Bibtex

Abstract

The paper presents the problem of position control of DC motor with rated voltage 24 V loaded by flywheel. The fractional order PD controller implemented in National Instruments NI ELVIS II programmed in LabView is used for controlling. The simple method for determining stability regions in the controller parameters space is given. Knowledge of these regions permits tuning of the controller and ensures required the phase margin of the system.

Go to article

Authors and Affiliations

Andrzej Ruszewski
Andrzej Sobolewski
Download PDF Download RIS Download Bibtex

Abstract

The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.

Go to article

Authors and Affiliations

Andrzej Ruszewski
ORCID: ORCID
Download PDF Download RIS Download Bibtex

Abstract

The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.

Go to article

Authors and Affiliations

Tadeusz Kaczorek
ORCID: ORCID
Andrzej Ruszewski
ORCID: ORCID
Download PDF Download RIS Download Bibtex

Abstract

The exponential decay of transient values in discrete-time nonlinear standard and fractional orders systems with linear positive linear part and positive feedbacks is investigated. Sufficient conditions for the exponential decay of transient values in this class of positive nonlinear systems are established. A procedure for computation of gains characterizing the class of nonlinear elements are given and illustrated on simple example.
Go to article

Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID
Andrzej Ruszewski
1
ORCID: ORCID

  1. Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D,15-351 Białystok, Poland
Download PDF Download RIS Download Bibtex

Abstract

The asymptotic stability of fractional positive descriptor continuous-time and discretetime linear systems is considered. New sufficient conditions for stability of fractional positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of fractional continuous-time and discrete-time linear systems.
Go to article

Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID
Andrzej Ruszewski
1
ORCID: ORCID

  1. Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
Download PDF Download RIS Download Bibtex

Abstract

The Floquet-Lyapunov transformation is extended to fractional discrete-time linear systems with periodic parameters. A procedure for computation of the transformation is proposed and illustrated by a numerical example.
Go to article

Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID
Andrzej Ruszewski
1
ORCID: ORCID

  1. Bialystok University of Technology, Faculty of Electrical Engineering,Wiejska 45D, 15-351 Białystok, Poland

This page uses 'cookies'. Learn more