Quadratic Stability with Performance control techniques are used to design controllers for the benchmark problem in the control of the wind excited tall building. The underlying quadratic stability framework can be used for a multi criterion approach which allows inclusion of variety of bojectives simultaneously. It is assumed that the building is equipped with active tunned mass damper (ATMD), and several designs which corresponds to different design tradeoffs, will be obtained and analyzed. The general solution and design of the compensator rely on the convex optimization techniques, through a number of matrix inequalities which contain the desired compensator matrices.
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