H<inf>&#x221E;</inf> observers design for a class of discrete time nonlinear singular systems

Abstract

In this paper the H∞ observers design problem for a class of discrete time Lipschitz nonlinear singular systems is considered. The approach is based on the parameterization of the obtained algebraic constraints from the estimation errors. Sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given. The method also unifies the design for the fullorder, reduced-order, minimal-order observers for discrete time systems. Application to standard systems with unknown input is presented via a numerical example.

Fault diagnosis for discrete-time descriptor linear systems

“…Remark 1. a • The observer (3)-(5) is represented in a general form and generalizes the existing ones. In fact: 6 For H = 0, S = 0, M = 0, and L = 0, then the following observer is obtained ζ(k + 1) =Nζ(k) + F a y(k) + Ju(k) χ(k) =P ζ(k) + Q a y(k) which has the form of the PO for descriptor systems (Darouach et al, 2010) 6 For P = I, L = 0 and let S = −C, and M = −CQ + I, then the following observer is obtained ζ(k + 1) =Nζ(k) + Hv(k) + F y(k) + Ju(k) v(k + 1) =y(k) − Cx(k) χ(k) =ζ(k) + Qy(k) which is the form used for the unknown input PIO for descriptor systems. Now, we the following lemma is considered.…”

“…These systems were introduced by Luenberger (1977) from a control theory point of view and since, great efforts have been made to investigate descriptor systems theory and their applications (see Müller and Hou (1993); Müller (2005); Liu et al (2008); Boulkroune et al (2009);Darouach (2009) ;Zhou and Lu (2009); Darouach (2012); Araujo et al (2012)). The main contribution of this paper is the new observer structure, which is more general than those presented in Darouach et al (2010) and Wu et al (2009). The aim of this work is to develop a fault estimation method for discrete-time descriptor systems.…”

Actuator and Sensor Fault Reconstructions for Uncertain Lipschitz Nonlinear Systems Based onH∞Observers

“…Most results focused on unknown input detection or reconstruction without considering the sensor fault, or coping with sensor faults without dealing with the unknown input. A few works that consider both unknown input and sensor faults simultaneously can be found in the literature [30][31][32][33][34][35][36][37][38][39][40], especially [30][31][32][33][34], which are based on H ∞ observers. Among the results, the reconstruction of both the unknown input and the sensor fault have been considered [33,35,36,40].…”

“…Among the results, the reconstruction of both the unknown input and the sensor fault have been considered [33,35,36,40]. For instance, [30][31][32] designed H ∞ observers for singular systems, where the disturbance or nonlinearities exist both in the state and output equations; however, the unknown input estimations were not considered. Reference [33] proposed an H ∞ sliding mode observer for simultaneous state and disturbance estimation for uncertain systems via singular system theory, where the unknown input is estimated based on equivalent output injection signal.…”

Observer design for discrete fuzzy time-delayed descriptor systems

“…As for observer design for discrete-time descriptor systems, little attention has been received. And only a few results have been published to talk about designing observers for discrete-time nonlinear descriptor systems [9,10]. As a result, it is necessary for us to derive a novel algorithm to design observer for discrete-time descriptor systems.…”