On the practical estimation of unknown inputs for polytopic LTI systems

Abstract

Reconstruction of unknown inputs is an important issue in real-time monitoring when they cannot be directly measured. This study proposes a coupled robust observer to estimate both the state vector and the unknown input of uncertain linear and time invariant (LTI) systems. A Luenberger observer is first considered to estimate the state vector and then, a super-twisting observer uses the precedent estimations to reconstruct the unknown input. Two semi-definite optimisation problems are proposed to compute the observer gains. The feasibility of the strategy is illustrated by the two examples, one of them a non-linear biological system.