On optimal damping of vibrating structures

The paper deals with the problem of optimal damping of vibrating structures by means of collocated decentralized devices. We consider both H2 and H∞ criteria. We prove that in the H2 case the problem can be conduced to the minimization of a function which is the sum of a convex and a concave component. This structure is of help in the solution of the problem. In the H∞ case we show that there exists at most a local minimum for the problem, at least in the single-parameter case. We finally apply the results to the switching case, which is a promising approach in term of performance improvement. © 2011 IFAC.