Maximal stability bounds of singularly perturbed systems

The maximal stability bound epsilon* of a linear time-invariant singularly perturbed system is derived in an explicit and closed form, such that the stability of the systems is guaranteed for 0 less than or equal to epsilon < epsilon*. Two new approaches including time- and frequency-domain methods are employed to solve this problem. The former leads to a generalized eigenvalue problem of a matrix pair. The latter is based on plotting the eigenvalue loci of a real rational function matrix derived by an LFT description system. The results obtained are coincident. Two illustrative examples are given to show the feasibility of the proposed techniques. (C) 2000 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.