A high-gain-based global finite-time nonlinear observer

Abstract

In this paper, a global finite-time observer is designed for a class of nonlinear systems with bounded rational powers imposed on the incremental nonlinearities. Compared with the previous global finite-time results, the new observer designed here is with a new gain update law. Moreover, an example is given to show that the proposed observer can reduce the time of the observation error convergence.

Continuous observer design for a class of multi-output nonlinear systems with multi-rate sampled and delayed output measurements

“…For example, the dynamical equations of a permanent magnet stepper motor can be transformed into the block lower triangular form (Mahmoud and Khalil, 2002). The estimation errors can converge to the origin in finite-time by using high gain observers in conjunction with applications of geometric homogeneity and Lyapunov theories (Shen and Xia, 2008;Shen and Huang, 2009;Li, Xia and Shen, 2013).…”

Uniformly convergent sliding mode-based observation for switched linear systems

“…A number of continuous, finite‐time converging, nonlinear observers have been proposed in recent years, mostly exploiting the properties of homogeneous vector fields (e.g., . Continuous finite‐time observers, however, suffer of a lack of robustness in that they only converge to a residual set centered around the origin when mismatches between the actual and nominal models, due to, for example, parameter uncertainty or perturbations, occur.…”

“…This is clear for instance from Pettersson [30], where the author focuses on the continuous-time estimation problem and shows that a bound to the estimation error can be given if the discrete mode is estimated correctly within a certain time. Additionally, for those switched systems admitting a dwell time, a guaranteed convergence of the discrete mode estimation taking place 'sufficiently faster' than the dwell time is required.A number of continuous, finite-time converging, nonlinear observers have been proposed in recent years, mostly exploiting the properties of homogeneous vector fields (e.g., [31][32][33][34][35][36]. Continuous finite-time observers, however, suffer of a lack of robustness in that they only converge to a residual set centered around the origin when mismatches between the actual and nominal models, due to, for example, parameter uncertainty or perturbations, occur.…”

Finite memory state observer design for polytopic systems. Application to actuator fault diagnosis

“…This filtering technique applied for the continuous case [10], [11] as well as for the discrete one [12], [13], offers a generic aspect in the sense that it is applied for state estimation, parameter estimation and control with sliding horizon. Note that the nonlinear case has been less discussed, however one can refer to the following works [14], [15], [16]. Several works based on sliding horizon for an exact state reconstruction in a finite time (without measurement noise nor model uncertainties) may be found in the literature with different terminologies like exact observers, FMO, integral observers and ideal observers.…”