On the simultaneous state and unknown input estimation of complex systems via a multiple model strategy

This study addresses the analysis and design of unknown input observer in order to provide both state and unknown input estimations of complex systems modelled with the help of a particular class of multiple model. The proposed observer uses the multi-integral strategy successfully employed in the classic linear control theory and known for its robustness properties. The observer design is based on the representation of the system via a particular multiple model, known as dasiadecoupled multiple modeldasia. This structure of multiple model allows to use submodels with different number of states and this feature constitutes the main advantage of the proposed observer with respect to the classic multiple model structure where the submodels have the same dimension. It is shown how the gains of the suggested observer can be obtained by solving a linear matrix inequality optimal problem. An academic example is also proposed in order to illustrate the proposed methodology.