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 non-preservation of the parameter uncertainty time dependency and the wrapping effect. Furthermore, $H_{\mathrm{\infty }}$ 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.

Keywords:

• Uncertain dynamic system
• interval observers
• time-invariant and time-varying uncertainties
• LMI technique
• $H_{\mathrm{\infty }}$ performance

Acknowledgements

This work has been partially funded by the Spanish Government (MINECO) through the project DEOCS (ref. DPI2016-76493-C3-3-R), by MINECO and FEDER through the project SCAV (ref. MINECO DPI2017-88403-R) and by Agència de Gestió d'Ajuts Universitaris i de Recerca. Furthermore, the authors thank Brais Gonzàlez García for his contribution in designing the real experiments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 OK

2 This approach is deeply investigated in Puig et al. (2003).

3 An interval hull of a set is defined as the smallest centred interval vector that contains the set.

4 This part shows the effect of the uncertainties since the deterministic approach is used.

5 An interval matrix is a matrix whose elements are interval numbers (Ganesan, 2007).

Additional information

Funding

This work has been partially funded by the Spanish Government (MINECO) through the project DEOCS (ref. DPI2016-76493-C3-3-R), by MINECO and FEDER through the project HARCRICS (ref. DPI2014-58104-R) and by Agència de Gestió d'Ajuts Universitaris i de Recerca.