Singular System Full-Order and Reduced-Order Fixed-Time Observer Design

This paper is concerned with the fixed-time observer (FTO) design for linear time-invariant singular systems. The advantage of the classical FTO technique is that it can reach accurate estimations of the states in an arbitrarily pre-defined time. However, the classical FTO method is only applied to non-singular systems. In order to overcome this restriction, new observer structures with respect to full-order and reduced-order FTOs respectively, are proposed. And, under the sufficient conditions we give, both the full-order and the reduced-order FTOs can indeed achieve accurate estimations in the fixed time we pre-set for the singular systems under consideration. Another advantage of the FTO is that both the estimation accuracy and the convergence time can be guaranteed regardless of whatever the initial values of the observer are. Finally, a numerical simulation validates the effectiveness of the proposed result.