Low-power peaking-free high-gain observers

Output Injection Filtering Redesign in High-Gain Observers

“…On the other hand, bound (6) highlights that the asymptotic gain at high-frequencies is proportional to k n and not to k n−1 . Nevertheless, as showed in [15], it can be shown that augmenting the relative degree between the measured output and the state estimations, may improve the asymptotic estimation (6). For this reason, in this work, we propose to redesign the observer (3) by augmenting the relative degree between the measured output and the estimates.…”

“…In this case, the choice of the matrix coefficients must satisfy a necessary condition, which is fully exploited. With respect to [12]- [15], the procedure of selection of the coefficients in the proposed structure is much simpler. Simulations are enclosed at the end of the work.…”

On Hamilton-Jacobi Approaches to State Reconstruction for Dynamic Systems

“…Unfortunately, the proof of stability of the estimation error is not easy for such estimators owing the need to have at disposal an analytic expression of vðt,xÞ. In practice, under general assumptions, one can find only approximate solutions to the HJ equation (11) and hence derive only local stability results [28], whereas, in general, global properties are preferable [29]. This motivates the investigation of the global stability properties that can be ensured by estimators having a structure like that in (18), as shown in the next section.…”

“…Specifically, we will focus on estimation for a class of nonlinear systems by using adaptive high-gain observers. Based on the pioneering work of Gauthier and Kupka [6], high-gain observers have achieved a lot of success (see, e.g., [7][8][9][10][11][12]).…”

Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities

“…Among others, the so-called high-gain observer has become quite popular [30], especially for the purpose of output feedback control [31]. More recently, Lyapunov functionals have been proposed in [32] to prove stability for time-varying high-gain observers in line with the idea of reducing the peaking during the transient [33,34].…”