Symbolic manipulations and numerical optimization techniques for robust eigenstructure assignment in LQR design of multivariable control systems

Design techniques to satisfy closed-loop eigenstructure requirements in linear quadratic regulator (LQR) synthesis of multivariable control systems are considered. A design algorithm for eigenstructure assignment (eigenvalue and eigenvector placement) which combines analytical methods implemented via symbolic manipulations and numerical optimization procedures is presented. The methods are indirect in that the eigenstructure assignment is achieved without actually carrying out LQR synthesis but in such a way as to guarantee that the control law could be obtained from LQR synthesis. Elements of the feedback gain matrix or the Riccati matrix are used as design variables while the Kalman inequality or the Riccati equation is used as a constraint to ensure robustness. Several illustrative examples are presented