Displaying similar documents to “Some remarks about a paper by T. Kaczorek and T. Traczyk”

Positive stable realizations of fractional continuous-time linear systems

Tadeusz Kaczorek (2011)

International Journal of Applied Mathematics and Computer Science

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Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.

New stability conditions for positive continuous-discrete 2D linear systems

Tadeusz Kaczorek (2011)

International Journal of Applied Mathematics and Computer Science

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New necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays

Tadeusz Kaczorek (2012)

International Journal of Applied Mathematics and Computer Science

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A new modified state variable diagram method is proposed for determination of positive realizations of linear continuoustime systems with delays in state and input vectors. Using the method, it is possible to find a positive realization with reduced numbers of delays for a given transfer matrix. Sufficient conditions for the existence of positive realizations of given proper transfer matrices are established. The proposed method is demonstrated on numerical examples.

Descriptor fractional linear systems with regular pencils

Tadeusz Kaczorek (2013)

International Journal of Applied Mathematics and Computer Science

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Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

Canonical forms of singular 1D and 2D linear systems

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

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The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for...