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2 Kaczorek T.

2 2012

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

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 4

897-905

A new modified state variable diagram method is proposed for determination of positive realizations of linear continuous-time 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.

Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

Kaczorek T.

Archives of Control Sciences

2012

Vol. 22, no. 4

451-465

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.