The influence of finite word length on digital optimal control

This paper is concerned with the performance of linear discrete-time systems, controlled by a finite word length computer with floating-point arithmetic, and of which the state is directly measurable with an A/D converter of the same word length. The effect of using finite word length is twofold. First, roundings are made after addition or multiplication of two rounded numbers. Second, the control parameters are represented in the controller's memory, by rounded numbers. The first effect can be accounted for by considering the control parameters stochastic. The second effect is deterministic. After a description of the stochastlcs of the roundoff errors has been derived, the influence of both effects on the optimality and stability of digital control systems in the steady state in relation to a quadratic cost function is considered.