Continuity of optimal robustness and robust stabilization in slowly varying systems

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 required for certain H” adaptation schemes for slowly varying systems. On the other hand, the S-suboptimal central design is shown to be Lipschitz continuous. Applications of the continuity properties and frozen-time stability analysis lead to a suboptimal design for robust stabilization in slowly time-varying plants which are represented by local normalized coprime factorizations.