Robust stability for linear discrete-time systems with structured perturbations

The robust stability problems of linear discrete-time systems with structured perturbations are considered. The necessary and sufficient condition of interval stability is given and the maximal bound of robust stability is presented for systems with a non-negative or non-positive nominal system matrix. Further, it is shown that the given necessary and sufficient condition and the given maximal robust bound are still valid for time-varying perturbations and nonlinear perturbations.