Multi-criteria problems for optimal protection of elastic constructions from vibration

In a multi-objective formulation with criteria such as the maximal deformation of the elastic object to be protected and maximal forces created by protection devices, a new class of optimal vibration protection problems is considered. A general approach to solving these problems based on results of modern control theory using linear matrix inequalities technique is presented. An example of a solution of two-criteria problem for a high-storey building under seismic disturbances is given.