System structure and structural index

In the case of descriptor systems, phenomena can occur that are in principle not possible for state-space representations. For example, under certain circumstances, small perturbations at the input can cause arbitrarily large errors in the solution. A quantity that qualitatively describes significant problems of the concrete descriptor system is the index. On closer inspection, the index is only one quantity among various structural indices which, in the case of linear time-invariant systems, can be described by the Weierstrass or Kronecker normal form. These normal forms can be understood as generalizations of the Jordan normal form for matrices to regular and singular matrix pencils.


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