Stability bounds for discrete-time singularly perturbed systems

The problem of evaluating the stability bounds of discrete-time singularly perturbed systems (slow sampling rate model) has been considered. A direct method for obtaining the maximal value ε₀ of the singular perturbation parameter ε has been developed, using the critical stability criteria, for which the overall system will remain stable ∀ε∈[0,ε0). It appears that the proposed method is more efficient than that suggested by Li and Li (1992) and completely removes the computational complexity associated with the quadratic dependence on the system matrix A(ε)