Synthesis of Non-Integer Order Uncertain Thau-Luenberger Observer for Non-Integer Order Multiple Model with Unknown Inputs

The present work introduces a novel method for state estimation of physical systems represented by an uncertain Non-Integer Order Multiple Model (NIO-MM) model with unknown inputs. The key concept underlying this approach involves formulating a non-integer order Thau-Luenberger Observer (NIO-TLO) designed specifically for the NIO-MM. This observer is developed to handle situations where both known and unknown inputs are subject to uncertainties, and the model itself incorporates bounded unknown inputs. The analysis of the convergence of the error of the state estimation is presented through the formulation of linear matrix inequalities (LMIs). To validate the proposed approach, an academic example is examined.