Normal Rank Ē$$ \bar{E} $$‐Order Interval Observer Design for Continuous Linear Time‐Invariant Systems With Unknown Input and Bounded Disturbances

ABSTRACT In this paper, an interval observer for continuous linear time‐invariant systems with unknown input and bounded disturbances is proposed. Usually, the design of such observers is based on the cooperative property of the considered system dynamics, which is hard to satisfy in many cases. To overcome this issue, in a recent work, it has been shown that under some assumptions, the cooperativity of the studied system can be ensured by means of a time‐varying change of coordinates. However, a constructive method for the design of the observer gain, making the observation error dynamics simultaneously positive and stable, is still missing and remains an open problem, especially in the context of unknown input. In this paper, a constructive approach is provided to obtain not only the observer gain but also a new gain that cancels the unknown input of the system and reduces the effect of the bounded disturbances. The proposed approach also allows for estimating the bounds of the unknown input. The efficiency of the proposed methodology is shown through numerical simulations and is compared with simulations resulting from a new method proposed in a recent work.