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Summary: This paper proposes a method to synthesize controllers that minimize an upper bound on the closed‐loop H2‐norm while imposing desired controller conic bounds. An initial conic controller is synthesized and iteratively improved. Conic sectors can be used to characterize a variety of input‐output properties, such as gain, phase, and minimum gain. If such plant properties hold robustly to uncertainty present, then closed‐loop stability can be ensured robustly via the Conic Sector Theorem by imposing desired controller conic bounds. Consequently, this paper provides a versatile optimal and robust controller synthesis method. Moreover, it relies only on the solution of convex optimization problems subject to linear matrix inequality constraints, making it readily implementable. [ABSTRACT FROM AUTHOR]

In order to ensure input–output stability for plants experiencing passivity violations, this paper explores the use of the conic sector theorem for both stability analysis and controller design. Given a previously designed controller and a plant that has experienced a (partially unknown) passivity violation, a novel conic bound selection procedure is presented. This procedure can be used to assess input–output stability of the violated plant and original controller via the conic sector theorem. Should input–output stability not be ensured, two original controller synthesis methods are suggested: one is designed to mimic thecontroller, and the other is inspired by strictly positive real controller synthesis. Both methods guarantee input–output stability by selecting controllers within appropriate conic sectors, and involve only the evaluation of readily solvable linear matrix inequalities and algebraic Riccati equations. Along with details on computational considerations, numerical simulations are provided, demonstrating the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]