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3 Kaczorek T.

3 2011

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Positive stable realizations of fractional continuous-time linear systems

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 4

697-702

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.

Computation of positive stable realizations for linear continuous-time systems

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2011

Vol. 59, nr 3

273-281

Conditions for the existence of positive stable realizations with system Metzler matrices for proper transfer function are established. It is shown that there exists a proper stable realization of transfer function of second order if and only if the transfer function has real negative poles. Sufficient conditions for the existence of positive stable realizations of transfer function of third order are established. A method based on the decomposition of transfer functions into the first, second and third orders transfer functions for computation of positive stable realizations is proposed. A method for computation of positive stable realizations of transfer functions with real negative poles and zeros is given.

Positive stable realizations with system Metzler matrices

Kaczorek T.

Archives of Control Sciences

2011

Vol. 21, no. 2

167-188

Conditions for the existence of positive stable realizations with system Metzler matrices for linear continuous-time systems are established. A procedure for finding a positive stable realization with system Metzler matrix based on similarity transformation of proper transfer matrices is proposed and demonstrated on numerical examples. It is shown that if the poles of stable transfer matrix are real then the classical Gilbert method can be used to find the positive stable realization.