Roundoff noise minimization in closed-loop systems using optimal error feedback and realization

We investigate the problem of optimizing error-feedback and realization to minimize the roundoff noise subject to l2-scaling constraints in a system in which full-order state observer feedback is used in place of system state feedback. In this paper, the optimal error-feedback matrix is determined in closed-form in advance. As a result, joint optimization of error-feedback and realization is no longer required. An iterative optimization technique for obtaining the optimal coordinate transformation matrix that minimizes the roundoff noise subject to l2-scaling constraints is explored by emplying a quasi-Newton algorithm. We also describe a separate optimization technique for comparison purposes. The results of numerical experiments demonstrate the validity and effectiveness of the proposed technique.