A Mixed Probabilistic/Deterministic Approach to Fixed Order H∞ Controller Design

This paper provides a mixed probabilistic/deterministic approach to design a fixed order H_∞ controller for a single-input single-output plant. A randomized algorithm is introduced to overcome the computational limitation of fully deterministic approaches, while a deterministic algorithm is partially employed to reduce the number of randomized parameters. A key feature of the proposed algorithm is to look for a probabilistic solution with a specified confidence, which means that a probabilistically arbitrarily exact result can be obtained for the fixed order H_∞ controller design within a computational time polynomially dependent on the problem size. The approach is an extension of a work previously proposed for stabilization. A key idea is to classify the controller parameters into two classes: intractable parameters and tractable parameters. The intractable parameters are chosen by a randomized method. Once the intractable parameters are fixed, convex characterization is possible for the tractable parameters that attain the desired H_∞ performance. This characterization is exploited for efficient design of the tractable parameters