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In this paper a full-order observer is suggested in order to achieve finite-time reconstruction of the state vector for a class of linear systems with unknown inputs. The proposed design procedure is a combination of the approaches proposed by Lin & Wang [1] and Trinh & Ha [2]. The resulted observer has been improved, from the robustness point of view, by this paper's authors by using a novel and efficient method; it consists of adding three robustness terms which cancel the negative effect of the uncertainties which can appear in the system. The effectiveness of the suggested design algorithm is illustrated by a numerical example (aircraft lateral motion).

The paper presents a new reduced-order multiple observer which can achieve the finite-time reconstruction of the system’s state associated to a multiple-model. This observer is a combination of a reduced-order observer and a full-order multiple observer. The design of the new observer involves the usage of the Lyapunov theory, the solving of a linear matriceal inequality, and a variables’ change. The steps of the design procedure have been software implemented in order to validate the new reduced-order multiple observer for the case of an aircraft motion during landing.