Less-conservative reduced-order interval estimation: A new two-step approach

This article proposes a two-step interval estimation method for continuous-time linear time-invariant systems with unknown but bounded disturbances and measurement noise. In the first step, H infinity$$ {H}_{\infty } $$ method is used to design a robust reduced-order observer that attenuates the impact of the system uncertainties on the estimation error. In the second step, a non-conservative interval prediction of the estimation error is achieved by applying a symmetric set-integration approach. The resulting tight set-valued state estimation is obtained by combining the point estimation from the reduced-order observer with the predicted estimation error set provided by the set-integration method. Compared to the conventional methods, the proposed method is built on less-restrictive design conditions, that allow one to deal with a large range of applications. On the other hand, numerical simulations show that the proposed method offers more precise interval estimation compared to an optimal reduced-order interval observer selected from recent literature.