Math. Systems Theory 22, 255-273 (1989) Mathematical Systems Theory © 1989 Springer-Verlag New York Inc. Optimal q-Markov COVER for Finite Wordlength Implementation Darrell Williamson 1 and Robert E. Skelton 2 i Department of Systems Engineering, Research School of Physical Scien~s, Australian National University, Canberra, ACT 2601, Australia z School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907, USA Abstract. The existing q-Markov COVER realization theory does not take into account the problems of arithmetic errors due to both the quantization of states and coefficients of the reduced-order model. All q-Markov COVERs allow some freedom in the choice of parameters. In this paper we exploit this freedom in the existing theory to optimize the models with respect to these finite wordlength effects. Introduction An asymptotically stable system can be characterized in terms of its impulse response sequence (Markov parameters) and its output covariance sequence (covariance parameters) due to a zero mean white-noise input process. A general approach has been developed [KDS] for realizing a system which matches q- Markov parameters and q-covariance parameters. Such a system is referred to as a q-Markov COVER, and q-Markov COVERs may be generated from output data FKDS], [SA] or from higher-order models FSC], [AS]. The Markov and covar- iance parameters are not independent and consequently the q-Markov COVER is not unique. In particular, all q-Markov COVERs are not related by state space similarity transformations [SA-I. In this paper we exploit the remaining degrees of freedom to optimize the q-Markov COVER realization with respect to an aspect of its finite wordlength realization. Specifically, when digital controllers are to be implemented, both the controller coefficients and the controller states must be represented in finite wordlength precision. This finite wordlength (FWL) representation (or quantization) causes inaccuracies in the response when compared with the ideal (i.e., infinite precision)