Guaranteed Interval State Estimation for Linear Parameter Varying Systems with Unknown Inputs

This paper investigates the construction of interval state observer for Linear Parameter Varying (LPV) systems affected by Unknown Input (UI) and bounded perturbations in both state and measurement equations. The parameter may depend on measurement or other exogenous measurable variables and is bounded in a compact set. The use of Sobolev spaces frame as well as High Order Sliding Mode (HOSM) differentiator enables us to properly access to the successive output derivatives, and thus to obtain an easily attainable rank condition for the decoupling of the UI from the state estimation error. In particular, the proposed rank condition relaxes the classical and widely used one. An interval state observer is provided and its boundedness is proved. Finally, an example illustrates the theoretical contribution.