Structural sensitivity analysis in a certain class of linear systems

It is well-known that many systems can be modelled as a set of linear algebraic equations. Such a set of equations can be represented by a directed graph, the so-called signal flowgraph (SFG). Using the concept of directed graph decomposition into irreducible subgraphs, which represent irreducible subsystems, it can be shown that the sensitivity of a solution to the changes of the system parameters strongly depends upon the internal structure of the system, as well as on the position of the changing parameters in the structure.