Structural decomposition of multivariable descriptor systems with inconsistent initial condition

Inconsistent initial condition of descriptor systems results in distributional solution. In general, it is hard to see the impact of inconsistent initial condition from the original form of the descriptor systems. We propose in this paper a structural decomposition algorithm for the multivariable descriptor systems. We simplified the structural decomposition by eliminate the zero part x_z in the decomposition. Under such a structural decomposition, the impact of inconsistent initial condition can be explicitly captured and displayed.