Phase-variable canonical form for time-varying multivariable systems

For time-varying multivariable systems, a phase-variable canonical form is presented. In comparison with the form of Luenberger (for time-invariant systems), the present förm is simpler in its structure and requires less computational effort for its determination. This simplification is due to a suitable choice of the order of the subsystems in the phase-variable form. This choice permits a useful subdivision of the control-lability matrix, which serves as the transformation matrix. In this way it is possible to compute directly the coefficients of the phase-variable form using matrices only of the order of the subsystem.