Realization Problem for Positive 2D hybrid systems

The realization problem for 2D positive hybrid systems is formulated and a method for finding a positive realization of a given proper transfer matrix is proposed. Sufficient conditions for the existence of a positive realization of a given proper transfer matrix are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.

[1]  Tadeusz Kaczorek REALIZATION PROBLEM FOR POSITIVE MULTIVARIABLE DISCRETE-TIME LINEAR SYSTEMS WITH DELAYS IN THE STATE VECTOR AND INPUTS , 2006 .

[2]  R. Roesser A discrete state-space model for linear image processing , 1975 .

[3]  Luca Benvenuti,et al.  A tutorial on the positive realization problem , 2004, IEEE Transactions on Automatic Control.

[4]  Tadeusz Kaczorek Positive minimal realizations for singular discrete-time systems with delays in state and delays in control , 2005 .

[5]  Tadeusz Kaczorek Realization problem for positive discrete-time systems with delays , 2004 .

[6]  Tadeusz Kaczorek Positive 2D hybrid linear systems , 2007 .

[7]  J. Klamka Controllability of dynamical systems , 1991, Mathematica Applicanda.

[8]  Tadeusz Kaczorek Realization problem for positive linear systems with time delay , 2005 .

[9]  J. Kurek,et al.  The general state-space model for a two-dimensional linear digital system , 1985 .

[10]  Maria Elena Valcher,et al.  On the internal stability and asymptotic behavior of 2-D positive systems , 1997 .

[11]  V. M. Marchenko,et al.  On the observability of linear differential-algebraic systems with delays , 2006, IEEE Transactions on Automatic Control.

[12]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

[13]  T. Kaczorek Positive 1D and 2D Systems , 2001 .

[14]  T. Kaczorek,et al.  Reachability and minimum energy control of positive discrete-time linear systems with multiple delays in state and control , 2007 .