A simple algorithm for time scale separation

Gerschgorin's circle theorem is used to develop a simple algorithm for identifying time scales in linear systems. The similarity transformation of matrices is then used to partition the system matrix A, with each diagonal block of A corresponding to a different time scale. Sufficient conditions under which this technique is applicable are given. The tractability of this algorithm in comparison to those found in the literature is discussed. The proposed algorithm is particularly useful for reducing the computational cost involved in decoupling a given system into its fast and slow subsystems. Two numerical examples are given to illustrate the use of the method. It is apparent from these examples that this algorithm is simple, computationally cheap, and reliable. However, it may require preliminary transformations of the A matrix to ensure that Gerschgorin's circle theorem can be used.<>