Stability issues of finite precision state estimate feedback controller realizations for discrete time systems

Abstract

A designed stable control system may become unstable when the digital controller is implemented with a fixed-point processor due to the Finite Word Length (FWL) effects. The FWL stability behavior of the digital control system depends on the actually used state space realization of the digital controller. For digital state-estimate feedback controllers, a FWL stability measure is derived, and a simple method is developed to compute the value of this measure for a given realization. From the implementation point of view, a more important problem is to find the optimal realization that provides the cheapest implementation in terms of word length and yet guarantees the stability of the closed-loop control system. The optimal state estimate feedback controller realization problem is studied in this paper. It is shown that the problem can be formulated as an unconstrained nonlinear programming problem to which many existing optimization algorithms, such as simplex search method, can be applied successfully. The theoretical results are illustrated by an example.

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