Maximal stability bounds of discrete-time singularly perturbed systems

The exact stability bound of the parasitic parameter for a discrete-time singularly perturbed system is determined by the linear fractional transformation (LFT) framework. Two systematic approaches including time-domain and frequency-domain methods are proposed to solve this problem based on the unified LFT framework. One employs the Kronecker product of LFTs and the guardian map theory. The other is to plot the eigenvalue loci of a real rational function matrix. Two examples are given to show the feasibility of the approaches.