Upper bound mixed H2/H∞ control and integrated design for collocated structural systems

The present paper addresses the mixed H₂/H_infin norm analysis and feedback control design problem for structural systems with collocated actuators and sensors. The mixed norm formulation provides a trade-off measure of a system performance and robustness in the presence of uncertainties in the system model. First, we develop an explicit upper bound expression for the mixed H₂/H_infin norm of collocated structural systems and an explicit parametrization of output feedback control gains to guarantee such bounds. The results offer computationally efficient solutions for system analysis and multi-objective controller design that are especially suitable for large-scale collocated systems where traditional analysis and design methods fail. The second part of the paper uses the proposed bounds to address the simultaneous design of structural damping parameters and feedback control gains for optimized closed-loop mixed-norm performance. A linear matrix inequality (LMI) formulation is provided for the integrated damping and control gain optimization. Structural control design numerical examples are presented to demonstrate the advantages and computational efficiency of the proposed bounds and the integrated design approach.