Input Observability and Input Reconstruction

Active Fault Diagnosis and Major Actuator Failure Accommodation: Application to a UAV

“…Such an estimation is possible if these inputs are observable. The input observability problem was addressed by Patton in (Hou & Patton, 1998) who gave some necessary and sufficient conditions to prove input observability for linear time invariant systems with unknown initial conditions. As far as the observer is concerned, Xiong (Xiong & Saif, 2003) proposed an Unknown Input Decoupled Functionnal Observer (UIDFO) which has no boundedness conditions as for time varying inputs and does not require differentiation of the measured outputs.…”

“…• λM r − N r is a singular pencil and has a block diagonal structure, each block takes the form • λM c − N c is a singular pencil and has a block diagonal structure, each block takes the form : (Hou & Patton, 1998).…”

Observability of structured linear systems in descriptor form: A graph-theoretic approach

“…Moreover, no assumption is done on the rank of [sE λ − A λ ] neither on its main diagonal. Therefore, our approach is adapted to analyse the input observability (Hou and Patton, 1998) of systems with unknown inputs since we do not made any hypothesis on the regularity of system (Σ Λ ). The kind of observability we study is related to the right-hand side (r-h.s.)…”

Simultaneous Input and State Estimation for Linear Continuous-Time Systems: A System Augmentation Approach

“…Simultaneous input and state estimation (SISE) has received much research attention due to its vast applications in different research areas, e.g., input reconstruction [1], [2], input estimation in physiological systems [3], fault diagnosis [4], [5], robust state estimation [6]- [8], and descriptor state estimation [9]. Most of the above work are focused on either discrete-time systems or time-invariant continuous-time systems, and very few addressed for time-varying continuoustime systems.…”

“…In this regards, both the reduced-order observer [10]- [12] and the full-order observer [1], [11]- [14] were proposed. It should be noticed that, most of the above work are focused on robust state estimation; only the work of [1] and [14] explicitly estimate the unknown inputs. Furthermore, a common approach to facilitate the above UIOs design is to use state transformation techniques or complex matrix equations solving.…”