Abstract
This paper proposes a novel data-driven pole placement-based H-infinity controller synthesis framework for discrete-time systems, with a particular focus on structural vibration control under bounded disturbances. The proposed method integrates circular and ellipsoidal regional pole placement constraints with H-infinity performance specifications by employing dilated linear matrix inequalities (LMIs). Unlike conventional model-based approaches, the framework does not require explicit knowledge of the system matrices A and Bu, and relies solely on input–state measurement data together with prescribed bounds on disturbances and system states. A dilation technique in the LMI formulation is adopted to reduce conservatism in the multi-objective control problem, allowing the use of non-common Lyapunov matrices across different control objectives. Moreover, the full-block S-procedure and nested attractive ellipsoids methods are employed to account for unknown but bounded disturbances within the data-driven formulation. The effectiveness of the proposed controllers is validated through numerical studies, including benchmark examples and simulations on a four-storey structural model for active vibration control. The results show that the proposed approach yields less conservative solutions, improved transient performance, and mathematically guaranteed closed-loop stability and performance even for unstable systems.
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