Robust controller design for matrix second-order systems with structured uncertainty

Matrix second-order systems arise frequently in the formulation of dynamic systems in classical mechanics, robotics, aerodynamics and many others. Though formulation of the control design problem in matrix second-order form has many advantages, there is very little literature available on this topic-even for nominal case. In this paper, we design controller gains directly in matrix second-order formulation for robust stability in a specified range of parameter variations. The stabilizing controller gains for the entire parameter variations range are obtained from only two given extreme matrices without formulating or checking the stability of other vertex matrices of the family. The design algorithm is computationally efficient and simple.