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Consider a closed-loop interconnection of an unknown linear plant and a known linear stabilizing controller, and assume that some knowledge of the closed-loop system is available. Suppose-on the basis of that knowledge-the existing, still stabilizing, controller no longer provides a satisfactory closed-loop performance, and hence the use of a new controller appears attractive. This scenario is common in Multiple Model Adaptive Control and Iterative Identification and Control algorithms. Our results will provide assurance for the closed-loop performance before the insertion of a new controller, and complement our earlier results for guaranteeing closed-loop stability in advance.