Filtered High Gain Interval Observer for LPV Systems with Bounded Uncertainties

In this paper, a new High-Gain Interval Observer (HGIO) structure and its filtered version, named Filtered High-Gain Interval Observer (FHGIO), are proposed for a class of Linear Parameter Varying (LPV) systems subject to additive disturbances and measurement noise. Those uncertainties are assumed to be unknown but bounded with known values. The HGIO is based on a high-gain observer structure from which an interval formulation is deduced taking into account the uncertainties bounds. Then, the proposed HGIO is extended to incorporate a filter for the output estimation error, leading to the FHGIO design whose goal is to reduce the measurement noise amplification. Usually, the design of such interval observers is based on monotone systems theory which is hard to satisfy in many cases. In this paper, suitable changes of coordinates are used to overcome this limitation. Moreover, a sufficient condition for the non-divergence of the radius dynamics and a procedure to design the observers gains ensuring the stability are given for each observer. The efficiency of the proposed observers is illustrated through a simulation on a numerical example.