Conic-Sector-based control to circumvent passivity violations

This paper explores the use of the Conic Sector Theorem for both stability analysis and controller design. Ensuring input-output stability of plants experiencing passivity violations is the motivation behind this work. Given a previously designed controller and plant that has experienced a (partially unknown) passivity violation, a novel sector 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 the H₂ controller, 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 inequalities. A numerical simulation is provided as a proof of concept.