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Positive Minimal Realization of Continuous-Discrete Linear Systems with All-Pole and All-Zero Transfer Function

Sajewski Ł.

Acta Mechanica et Automatica

2013

Vol. 7, no. 1

42-47

The positive and minimal realization problem for continuous-discrete linear single-input and single-outputs (SISO) systems is formulated. Two special case of the continuous-discrete systems are given. Method based on the state variable diagram for finding a positive and minimal realization of a given proper transfer function is proposed. Sufficient conditions for the existence of a positive minimal realization of a given proper transfer function of all-pole and all-zero systems are established. Two procedures for computation of a positive minimal realization are proposed and illustrated by a numerical examples.

General Response Formula for Fractional 2D Continuous-Time Linear Systems Described by the Roesser Model

Rogowski K.

Acta Mechanica et Automatica

2011

Vol. 5, no. 2

112-116

A new class of fractional two-dimensional (2D) continuous-time linear systems is introduced. The general response formula for the system is derived using a 2D Laplace transform. It is shown that the classical Cayley-Hamilton theo- rem is valid for such class of systems. Usefulness of the general response formula to obtain a solution of the system is discussed and illustrated by a numerical example.

A new approach to physically based interpretation of experimental data in 2D problems in mechanics

Karmowski W., Midura G.

Computer Assisted Mechanics and Engineering Sciences

2006

Vol. 13, No. 4

547-556

The concept of experimental data interpretation in mechanics using Dirac function is presented. The objective is to find generał differential eąuation, which may be used to approximate the stress field sought. Application of this method may convert problem from generał spline to variational one. Basic idea has been presented earlier in [6] where both theoretical data and results of experiments have been taken into account. Herę, the method has been used to solve a 2D problem. Numerical tests performed for both generated and experimental data proved its usefulness.

Algorytm budowy "Węzeł po węźle" równań MES w obliczeniach równoległych problemów dwuwymiarowych

Detka M.

Zeszyty Naukowe. Budownictwo / Politechnika Śląska

2005

z. 104

75-82

W pracy wykorzystano metodę Free Mesh Method (FMM) [4, 5, 6] do rozwiązania dużego dwuwymiarowego problemu eliptycznego w środowisku klastra obliczeniowego, z wykorzystaniem systemu komunikatów MPI oraz pakietu do obliczeń równoległych PETSC. Algorytm FMM zmodyfikowano dla uniknięcia niejednoznaczności przy konstruowaniu lokalnej siatki elementów skończonych wokół węzła. Przykłady potwierdziły skuteczność poprawionego algorytmu i jego efektywność w obliczeniach równoległych.

In the paper, the Free Mesh Method (FMM), [4, 5, 6], is applied to the analysis of the large scale two-dimensional elliptic problems. The MPI environment and PETSC library is used. The original FMM algorithm has bee modified in order to avoid some inconsistency in generation of the mesh elements, around the nodes. The examples confirmed efficiency of the proposed method in the parallel computations.