An observer design for linear systems with unknown inputs

Full-order observers for linear systems with unknown inputs

“…Bhattacharyya [4] uses a geometric approach, while Miller and Mukundan [5] use the generalized inverse matrix. Kobayashi and Nakamizo [6] propose a procedure based on the Silverman's inverse method. Fairman et al [7] suggest an approach using the singular value decomposition.…”

Optimal state filter from sequential unknown input reconstruction: Application to distributed state filtering

“…Without communication between subsystems, Appendix A recalls the structural conditions under which d i,k can be reconstructed with finite structural delays α i from local measurements y i,k available until time k (see also previous works [25][26][27][28] ). This paper assumes that Equation 3 is left invertible with structural delays α i = 0 if rank(J i ) = q i (6) or when rank(J i ) < q i with structural delays…”

“…23 The problem of inverting linear time-invariant systems has been of interest to control engineers for many years. The existence conditions under which a linear discrete-time system with permanent unknown inputs is left invertible with zero, one or more structural delays has been discussed in previous works [25][26][27][28] or in Appendix A. This paper solves the autonomous distributed state filtering problem when subsystems are assumed to be left invertible.…”

H ∞ synthesis of unknown input observers for non-linear Lipschitz systems

“…This problem is also referred to as the unknown input observer (UIO) design and it dates back to 1975 where Wang (1975) proposed a minimal order UIO structure for linear systems with both known and unknown inputs. After this important work, several approaches for designing reduced order and full order UIOs have been proposed, including the geometric approach by Bhattacharyya (1978), the inversion algorithm by Kobayashi and Nakamizo (1982), the matrix algebra method by Watanabe and Himmelblau (1982), the singular value decomposition technique by Fairman et al (1984) and the algebraic approaches by Hou and Mu¨ller (1992) and Patton et al (1996) (see also Kudva et al 1980, Guan and Saif 1991, Darouach et al 1994, Hou and Mu¨ller 1994, for different UIO design techniques). Achieving less restrictive existence conditions and more direct design procedures has always been a challenge in this area.…”