Robust interval estimation of state and unknown inputs for linear continuous-time systems: An L₁gain characterization

This paper introduces a robust interval observer to address the problem of state and unknown input estimation for linear continuous-time systems subject to unknown but bounded disturbances and measurement noise. Firstly, a decoupling method is presented to reduce the unknown input effect on the state dynamics. This transforms the estimation problem into the design of an observer for a singular model representation. Secondly, we propose a continuous-time TNL approach that incorporates weighting matrices including the traditional gain of the observer for this singular system. A novel stability analysis for the error system utilizing the L₁ norm is used. Through a numerical example of a fifth-order lateral axis model of a fixed-wing aircraft system, the efficiency of the proposed design approach is illustrated.