Maximal stability bounds of singularly perturbed systems

The maximal stability bound ε∗ 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⩽ε<ε∗. 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.