CONVERSION OF DISCRETE-TIME TIME-INVARIANT LINEAR-SYSTEMS INTO CONTINUOUS SYSTEMS

When a discrete-time time-invariant linear system (DILS) is given (considered as a discretization of an unknown continuous-time time-invariant linear system (CILS) by a zero order hold), a practical method is proposed which decides the form of the original unknown CILS. The DILS is first transformed into Kalman canonical form by a suitable linear transformation. Next with the help of the matrix logarithm and the Dunford integral, the DILS in canonical form is converted into a CILS, which is in formal Kalman canonical form. Finally the last CILS changes into the definite form of the original unknown CILS by the transformation inverse to the above suitable linear transformation.