Numerical Approaches To Robust Partial Quadratic Eigenvalue Assignment Problems

Second-order control systems arise in a remarkable variety of applications such as large flexible space structure control,earthquake engineering,the control of flexible multibody systems,the controller design for damped gyroscopic systems,robotics,and the vibration in structural dynamics.In this thesis we consider the robust partial quadratic eigenvalue assignment problem for second-order control systems by state feedback.To reduce the feedback norms and sensitivity of the close-loop eigenvalues,we formulate the problem as two different unconstraint nonlinear minimization problems with new proposed cost functions.Explicit analytic expressions of the gradients of the cost functions are derived via the Sylvester equation-based parametrization. Then we employ gradient-based techniques to solve the minimization problems, Numerical tests are also reported to illustrate the effectiveness of the proposed approaches.