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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.