Identification of critical modes of large-scale systems excited with several input functions

The authors present a methodology for identifying the critical modes of large-scale systems excited by several input functions, including step and impulse functions. A quadratic performance measure is defined. This index is related to the type of application under consideration. For example, the index can be a function of the output variables or some other desired state variables. Each eigenvalue is evaluated by assessing its contribution to that performance index. The eigenvalues that contribute the most to the performance measure are identified as the critical modes. An algorithm is derived, and an example is given to illustrate the proposed method