Interval estimation based on the reduced-order observer and peak-to-peak analysis

Abstract

An interval estimation method based on the reduced-order observer and peak-to-peak analysis is proposed for continuous-time linear time-invariant systems with disturbance and measurement noise. The proposed method consists of two steps. First, a reduced-order observer with $L_{\mathrm{\infty }}$ performance is designed to obtain point estimation. Second, interval estimation is achieved by integrating the obtained point estimation and the error interval estimation by peak-to-peak analysis. Steady-state gain optimisation in terms of linear matrix inequalities is used in both steps to improve the estimation accuracy of the proposed method. The superiority of the method over the reduced-order interval observer is illustrated through numerical simulations.

Keywords:

• Reduced-order observer
• interval estimation
• peak-to-peak analysis

Disclosure statement

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

Additional information

Funding

This work was supported by the National Key R&D Program of China [grant number 2016YFB0501203] and by the National Natural Science Foundation of China [grant number 61973098].