Robust regional eigenvalue-clustering analysis for grey discrete-time systems with/without state delay

The regional eigenvalue-clustering robustness problem of grey discrete-time systems with/without state delay is considered. Based on both spectral radius approach and matrix measure approach, three new sufficient conditions are proposed to preserve the regional eigenvalue-clustering property of grey discrete-time systems with/without state delay. If all eigenvalues are only required to be located within the unit circle, the proposed criteria become stability criteria. The proposed sufficient conditions are mathematically proven to be less conservative than those reported in the literature. Three examples are given to demonstrate that the proposed sufficient conditions are applicable and obtain less conservative results compared with those reported recently in the literature.