Optimal error feedback and realization for roundoff noise minimization in linear discrete-time systems with full-order state observer feedback

The optimization problem of error-feedback and realization to minimize the roundoff noise in a closed-loop system with full-order state observer feedback subject to l₂-scaling constraints is investigated. It is shown that joint optimization of error-feedback and realization is not needed when utilizing a general-matrix error-feedback loop because the optimal error-feedback matrix, in closed-form, can be determined in advance. An analytic technique is developed for obtaining the optimal realization that minimizes the roundoff noise subject to l₂-scaling constraints. A numerical example is presented to demonstrate the validity and effectiveness of the proposed technique.