H∞ Observer Design for a Class of Nonlinear Discrete Systems

Abstract

In this paper, the problem of observing the state of a class of discrete nonlinear system is addressed. The design of the observer is dealt with using H∞ performance techniques, taking into account disturbance and noise attenuation. The result is an LMI optimization problem that can be solved by standard optimization techniques. A design strategy is proposed based on the available disturbances information.

A novel H∞ memory observer design for uncertain switched nonlinear systems using past output measurements

“…To this end, a robot trajectory tracking controller based on observer is proposed in Reference 26. Great progress has been made in the problem of $$$ {H}_{\infty } $$$ filtering and state observation for non‐switched systems 27‐32 . Without exception to the state estimation problem of switched systems, there have been abundant achievements in signal estimation for switched systems as well 21,33‐35 .…”

“…In Reference 31, a class of observers have been designed, and then a robust sliding mode $$$ {H}_{\infty } $$$ control method for stochastic Markovic jump systems has been proposed based on the estimation of the system state. The literature, 32 which has proposed three ways of considering Lipschitz nonlinear condition into matrix inequalities, has presented a designed approach of $$$ {H}_{\infty } $$$ state observer for nonlinear systems in consideration of disturbance and noise attenuation. In Reference 21, a nonfragile observer for switched nonlinear systems is proposed, which considers the scalar form of the Lipschitz nonlinearity.…”

Observers for nonlinear lipschitz discrete time systems with extension to H∞ filtering design

“…The H ∞ observer design for nonlinear discrete systems has been studied by several authors in the literature such as the work of [11]- [13]. The idea behind is to obtain information about internal variables which are not directly available at the output and they are corrupted by noise.…”

Robust output feedback control of 2D discrete systems with actuator saturation and time-varying delay

“…However, in practical systems, it is not necessary that all state variables are available for measurement, whereas the aforementioned works presume that all states of the system are available. The importance of an observer-based approach is interesting because the complete state of the system is not measurable in a real system due to corruption by noise or disturbances (Penarrocha et al, 2009). So, many research scholars have shown their keen interest in design of an observer-based H N controller (Penarrocha et al, 2009;Karimi, 2008;Chang and Yang, 2014).…”

“…The importance of an observer-based approach is interesting because the complete state of the system is not measurable in a real system due to corruption by noise or disturbances (Penarrocha et al, 2009). So, many research scholars have shown their keen interest in design of an observer-based H N controller (Penarrocha et al, 2009;Karimi, 2008;Chang and Yang, 2014). A static, dynamic and observer-based output feedback H N controller has been designed by Chang and Yang (2014) for a discretetime system, while a static output feedback H N controller has been designed for a continuous linear system with polytopic uncertainty (Chang et al, 2015).…”