Worst case estimation under model uncertainty

In system identification a dynamical model of a process is identified using measurement data. The uncertainties in the system parameters and the observation noise are described usually by stochastic mechanisms. However there are many situations where the main contribution to the error is not of a random nature and therefore cannot be suitably described by random noise. Thus statistical methods are not always appropriate for system modelling and identification. A theory, which assumes that there is no statistical description for the measurement noise or for the disturbances in the system, has been developed named theory of guaranteed identification or set-membership description of uncertainty or theory of difference inclusions. A considerable number of applications in engineering and systems analysis are treated under informational assumptions that justify this approach. In this paper we address the problem of deriving bounding parameter sets of state-space systems in the presence of bounded, uncontrolled but nonstochastic disturbances