A SOS-based robust fault detection method for polynomial nonlinear systems

A novel nonlinear Luenberger-like filter design method is discussed for fault detection of nonlinear polynomial systems subject to unknown inputs. The disturbance rejection/ fault sensitivity conditions are characterized by exploiting Algebraic Geometry methods. By means of the Positivstellensatz Theorem, a Sum of Squares (SOS) formulation of the design problem is obtained and an adaptive threshold is proposed to reduce the effect of false alarms. The effectiveness of the filter is illustrated via a numerical example taken from the literature.