Robust Stability Analysis of Interval Observer for Linear Continuous-Time Systems: An $L_{1}$-Gain Characterization

This paper aims to introduce a robust interval observer for linear continuous-time systems with unknown but bounded uncertainties. Firstly, we present a continuous-time TNL approach, named after the notation for the different used matrices, that incorporates weighting matrices alongside the traditional observer gain. This approach enhances the observer's performance. Secondly, we propose a novel stability analysis for the resulting error system, leveraging the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{1}$</tex> norm. The design conditions are formulated as a linear programming (LP) problem. Our method not only offers relaxed design conditions but also enhances the accuracy of interval estimation. Through a numerical example, we demonstrate the effectiveness and superiority of the proposed design approach.