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Due to the finite precision nature of computer arithmetic, the output roundoff noise of a fixedpoint IIR digital filter usually arises. This noise is critically dependent on the internal structure of an IIR digital filter [1],[2]. Error feedback (EF) is known as an effective technique for reducing the output roundoff noise in an IIR digital filter [3]-[5]. Williamson [6] has reduced the output roundoff noise more effectively by choosing the filter structure and applying EF to the filter. Lu and Hinamoto [7] have developed a jointly optimized technique of EF and realization to minimize the effects of roundoff noise at the filter output subject to l2-norm dynamicrange scaling constraints. Li and Gevers [8] have analyzed the output roundoff noise of the closed-loop system with a state-estimate feedback controller, and presented an algorithm for realizing the state-estimate feedback controller with minimum output roundoff noise under l2-norm dynamic-range scaling constraints. Hinamoto and Yamamoto [9] have proposed a method for applying EF to a given closed-loop system with a state-estimate feedback controller. This paper investigates the problem of jointly optimizing EF and realization for the closedloop system with a state-estimate feedback controller so as to minimize the output roundoff noise subject to l2-norm dynamic-range scaling constraints. To this end, the problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques, and then an iterative technique which relies on a quasi-Newton algorithm [10] is developed. With a closed-form formula for gradient evaluation and an efficient quasi-Newton solver, the unconstrained optimization problem can be solved efficiently. Our computer simulation results demonstrate the validity and effectiveness of the proposed technique. Throughout the paper, In stands for the identity matrix of dimension n × n, the transpose (conjugate transpose) of a matrix A is indicated by AT (A), and the trace and ith diagonal element of a square matrix A are denoted by tr[A] and (A)ii, respectively.

Roundoff Noise Minimization for State-Estimate Feedback Digital Controllers Using Joint Optimization of Error Feedback and Realization