Damping parameter design optimization in structural systems using an explicit H∞H∞ norm bound

This paper examines the damping parameter design optimization problem for structural systems with collocated measurements and inputs so that H∞H∞ norm bound constraints are satisfied. We utilize a particular solution of the Bounded Real Lemma that provides an explicit upper bound on the H∞H∞ norm of a collocated structural system. Using this upper bound result the damping design is formulated as a linear matrix inequality (LMI) optimization problem with respect to the damping coefficients of the structural system. The formulation is particularly useful for large-scale structural systems where existing methods are computationally prohibitive. Numerical examples demonstrate the benefits and computational advantages of the proposed damping parameter design method.