Stabilization of Nonlinear Dynamic Systems Using the System State Estimates Made by the Asymptotic Observer

Abstract

Consideration was given to asymptotic stabilization of the equilibria of nonlinear dynamic systems using the dynamic output feedbacks, that is, the feedbacks in the estimate of system state made by the asymptotic observer. Presented were the basic methods of constructing the asymptotic observers for the nonlinear dynamic systems with control and the approaches to system stabilization using the system state estimate made by the observer.

Observer-Based Controllers for Incrementally Quadratic Nonlinear Systems with Disturbances

“…with Γ i1 (i = 1, 2) given in (27) and Γ i2 (i = 1, 2) given in (28). Then, the closed-loop system (15) is ISS w.r.t.…”

“…for i = 1, 2, where Γ i1 , Γ i2 are given in ( 27), (28). Note that Γ i1 is invertible since T i is invertible.…”

“…There have been results on the controller-observer separation for different classes of nonlinear systems and proposed constructive methods for the observer and controller design; for instance, [17], [18] studied nonlinear systems with sloperestricted nonlinearities via the circle criterion, [19], [20], [21] investigated uniformly observable systems using highgain observers, [22], [23], [24] considered globally Lipschitz X. Xu nonlinear systems (also refer to [25], [26], [27], [28], [29], [30], [31] and references therein). In spite of those valuable results, there is still a need to explore more general classes of nonlinear systems for which their asymptotic observers and stabilizing state feedback controllers can be designed separately and constructively.…”

Postgraduate Education in Nonlinear Dynamical Systems and Automatic Control in Aerospace*

“…Nonlinear state observers and output feedback, see e.g. Besançon (2007), Golubev et al (2005), Khalil (2002) and Krstić et al (1995):…”

Design and applications of interval observers for uncertain dynamical systems

“…As such, transformation is based on the uncertain parameter or maybe unknown due to the complexity of the model; therefore, it can be an obstruction in practice to observers design. One can read the survey about the application of observers in the control and estimation of a non‐linear system for further study [15]. Another class of dynamical systems that can be used in several fields, such as electrical devices, flight control systems, congestion modelling and so on, is switched linear system (SLS).…”