Based on Lyapunov stability theory associated with transformation techniques, the D-stability robustness problem is first discussed for discrete large-scale systems subjected to interconnections and perturbations. Three classes of perturbation are treated: (1) unstructured parametric perturbations; (2) highly structured parametric perturbations; and (3) nonlinear perturbations. If all the eigenvalues of each nominal subsystem are located inside the specified discs Di(∝i, ri), respectively, sufficient conditions for D-stability are presented to guarantee that all the eigenvalues of each perturbed subsystem remain inside the same discs. Furthermore, the proposed D-stability criteria ensure that the whole discrete large-scale system is D-stable irrespective of perturbations and interconnections if the eigenvalues of each nominal subsystem lie within the same disk D(∝, r). By these conditions, the allowable perturbation bounds that ensure the D-stability of discrete large-scale perturbed system can be estimated. Finally, numerical examples are given for illustration.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Theoretical Computer Science
- Computer Science Applications