Continuity of optimal robustness and robust stabilization in slowly varying systems

The continuity properties of the optimal design of robust stabilization in the gap metric are investigated. In general, the optimal design in the gap metric lacks continuity properties arising in certain H^∞ adaptation schemes for slowly varying systems. The δ-suboptimal central design is shown to be Lipschitz continuous. Applications of the continuity properties lead to a suboptimal design for robust stabilization in slowly time-varying plants which are represented by local normalized coprime factorizations