Regularly persistent observers for bilinear systems

Observability of smooth control systems

“…In the last several years, a number of works appeared which contain investigations that characterize the part played by inputs in the problem of observer synthesis [63,76,88,89,134] and others.…”

“…The constructions of observers for systems with regularly persistent inputs were described in [63,88]. Let us consider the system…”

Residual generator design for singular bilinear systems subjected to unmeasurable disturbances: an LMI approach

“…Assumption 1 ensures that the contribution of the non-zero failures f 1(k) on the residual θ k is different from zero, and the residual θ k obtained from (12) and (16) fulfills condition (iii) in Definition 1. Notice thatV (e, u) is uniformly bounded with respect to u and the UIRG works for non-uniformly observable systems as well as the control input u belongs to Ω, even if u is a non-universal input (see (Bornard et al, 1988)). The design of the k th UIRG is decomposed in three parts.…”

“…Frank (1993) considered the residual observer for nonlinear systems using a first order approximation, then the stability of the observation error is local. Kinnaert et al (1995;1999) treated the failure detection and isolation problem for bilinear systems using the regularly persistent observers proposed in (Bornard et al, 1988). This approach is less restrictive than those proposed by Yu and Shields (1996).…”

Transformation to state affine system and observer design

“…High-gain observers are useful for state alZfine systems as shown in [3,12,30] and the references therein. These observers are based on optimal Kalman's observer and used in physical processes, for instance chemical reactors, distilling columns and mechanical systems [8, 30, I].…”