The solution of problems of control, observation of the initial state, parameter estimation and related topics can be optimized by using the freedom in the choice of the instants of sampling.
Summary--For linear multivariable control systems the question of observing the state by means of sampling with arbitrary but fixed choice of the sampling instants is discussed. The freedom due to this arbitrary choice is used to derive criteria for a choice of the sampling instants which is as advantageous as possible as far as the propagation of measuring errors is concerned. The extended principle of duality is formulated and the dual problem of control by means of step functions is covered. Further topics mentioned are e.g. the identification problem and the influence of uncertainties of parameters. sampling instants in this generalized case, too. But intervals can be specified, so that complete observability is preserved, if the sampling instants are taken out of such an interval. By the extended principle of duality there is also the possibility to make use of these results in the problem of (optimal) control. A further interesting application of these ideas is e.g. the identification problem.