On robust interval observer design for uncertain systems subject to both time-invariant and time-varying uncertainties

Abstract

This paper proposes the design of an interval observer-based approach for linear dynamic systems affected by both time-invariant and time-varying uncertainties. First, different interval observer schemes are compared and analysed when dealing with the different types of uncertainties. Then, an integrated interval observer is proposed in order to overcome the drawbacks of using the set-based approach, i.e. the nonpreservation of the parameter uncertainty time dependency and the wrapping effect. Furthermore, H ∞ performance is considered in order to compute the observer gain by using an LMI technique. Finally, a numerical example and a real case study based on a two-tank system are employed for both illustrating and analysing the effectiveness of the proposed approach.