The present thesis is concerned with different aspects of modelling, control
and identification of linear systems.
Traditionally, discrete-time sampled-data systems are represented using
shift-operator parametrizations. Such parametrizations are not suitable at
fast sampling rates. An alternative parametrization using the so-called
delta-operator is examined. It is shown how to maintain a close correspondence
to continuous-time when sampling a
system described in continuous-time by stochastic differential equations.
Using delta-operator parametrizations makes it possible to unify discrete-time
and continuous-time theory. In addition these parametrizations possess certain
numerical advantages compared to shift-operator representations.

A new prediction method is developed. It is based on ideas from
continuous-time but derived from
discrete-time delta-operator models. It is shown to
include the optimal minimum-variance predictor as a special case
and to have a well-defined continuous-time limit.

By means of this new prediction method a unified framework for discrete-time
and continuous-time predictive control algorithms is developed. This contains
a continuous-time like discrete-time predictive controller which is
insensitive to the choice of sampling period and has a well-defined limit in
the continuous-time case. Also more conventional discrete-time predictive
control methods may be described within the unified approach.
The predictive control algorithms are extended to frequency weighted criterion
functions. Also a state-space approach is described which extends
straightforwardly to the multi-variable case.

Finally, aspects on the connection between system identification and control
design are discussed. Several approaches to improve this interconnection
have been proposed. The frequency-distribution of the estimation error with
low-complexity models is treated and proves to be important for the
development of control-relevant prefilters in estimation. Iterative approaches
are presented, both using standard estimation methods with prefiltering and
non-standard control-relevant estimation methods. New combined
adaptive/iterative techniques are proposed.

### Ph.d thesis 27, 1997

Last modified January 12, 1999