Positive stable realizations with system Metzler matrices

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Positive stable realizations with system Metzler matrices

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.

L. Benvenuti and L. Farina: A tutorial on the positive realization problem. IEEE Trans. Autom. Control, 49(5), (2004), 651-664.

L. Farina and S. Rinaldi: Positive linear systems, Theory and applications. J. Wiley, New York, 2000.

T. Kaczorek: A realization problem for positive continuous-time linear systems with reduced numbers of delays. Int. J. Appl. Math. Comp. Sci. 16(3), (2006), 325-331.

T. Kaczorek: Computation of realizations of discrete-time cone systems. Bull. Pol. Acad. Sci. Techn. 54(3), (2006), 347-350.

T. Kaczorek: Fractional positive continuous-time linear systems and their reachability. Int. J. Appl. Math. Comput. Sci., 18(2), (2008), 223-228.

T. Kaczorek: Fractional positive linear systems. Kybernetes: The International J. of Systems & Cybernetics, 38(7/8), (2009), 1059-1078.

T. Kaczorek: Linear control systems, vol.1, Research Studies Press. J. Wiley, New York, 1992.

T. Kaczorek: Positive 1D and 2D systems. Springer-Verlag, London, 2002.

T. Kaczorek: Polynomial and rational matrices. Springer-Verlag, London, 2009.

T. Kaczorek: Realization problem for fractional continuous-time systems. Archives of Control Sciences, 18(1), (2008), 43-58.

T. Kaczorek: Realization problem for positive 2D hybrid systems. COMPEL, 27(3), (2008), 613-623.

T. Kaczorek: Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs. Int. J. Appl. Math. Comp. Sci., 16(2), (2006), 101-106.

T. Kaczorek: Realization problem for positive discrete-time systems with delay. System Science, 30(4), (2004), 117-130.

T. Kaczorek: Positive minimal realizations for singular discrete-time systems with delays in state and delays in control. Bull. Pol. Acad. Sci. Techn., 53(3), (2005), 293-298.

T. Kaczorek: Selected Problems in Fractional Systems Theory. Springer-Verlag, 2011.

U. Shaker and M. Dixon; Generalized minimal realization of transfer-function matrices. Int. J. Contr., 25(5), (1977), 785-803.

Archives of Control Sciences

The Journal of Polish Academy of Sciences

Journal Information

IMPACT FACTOR 2016: 0.705

CiteScore 2016: 3.11

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.565


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