Robust D-stability of discrete and continuous time interval systems

Necessary and sufficient conditions are presented for the robust Schur and Hurwitz stability of the dynamic interval systems. An interval matrix can be expressed as a linear fractional transformation of an interconnection matrix with structured real parametric uncertainties. Consequently, the robust stability problem is converted to a robust nonsingular problem. An explicit condition in terms of the structured singular value is provided to ensure the stability robustness of dynamic interval systems. This systematic approach is feasible for both discrete-time and continuous-time cases. The proposed technique can be applied directly to D-stability for performance requirements.