Robust observer design for a class of discrete‐time nonlinear singular systems with persistent disturbances

Abstract

SummaryThis article addresses the design of a nonlinear observer for nonlinear uncertain discrete‐time descriptor systems. The nonlinearities that appear in both state and output equations fulfill a Lipschitz‐like condition locally. Besides, the parametric uncertainties can affect the state dynamics as well as the input and output channels. The design methodology ensures input‐to‐state stability of the observer while minimizing an upper bound on a peak‐to‐peak performance index relating the disturbances/parametric uncertainties and the error in estimating a given performance signal. The observer design is cast as a convex optimization problem involving a set of linear matrix inequalities subject to a linear matrix equality constraint. The effectiveness of the proposed method is illustrated by numerical examples.

Static output-feedback peak-to-peak gain control of discrete-time positive linear systems with diverse interval delays

“…that makes the resulting closed-loop system positive, stable and has prescribed ' ' -gain performance, where K 2 R n u 3 n y is the controller gain which will be determined. By incorporating (26), the closed-loop system of (25) is presented as…”

“…However, in many engineering systems as wind shear on aircraft wings or continuous road excitation on vehicle suspension systems, external disturbances are generally persistent and amplitude-bounded rather than specifications on the total energy of a disturbance are required. 24–26 Thus, we only have estimations or measurements of peak values of associated input and output signals and the proposed control schemes involving information of signal total energy are no longer applicable. In such models, the worst case amplification from input disturbance to regulated output represents a reasonable performance index, which gives rise to the so-called peak-to-peak gain (also known as ℓ ∞ -induced) control problem.…”

Fault diagnosis by interval‐based adaptive thresholds and peak‐to‐peak observers

“…Vidyasagar et al 13 first introduce the peak-to-peak performance and this performance has been applied to the observer or residual generator design problems in many reports. [14][15][16] The peak-to-peak residual generator design aims to minimize the worst-case peak value of the residuals concerning peak bounded uncertainties. Following this purpose, Yang et al 17 utilized this peak-to-peak performance to design residual generators for a class of uncertain state-feedback control systems, which is then applied to the fault detection for flight control systems.…”

“…Instead, the peak‐to‐peak performance, which employs the peak values of signals and describes the peak‐to‐peak gain (also called the $$$ {L}_{\infty } $$$ gain) of systems, becomes more reasonable and useful. Vidyasagar et al 13 first introduce the peak‐to‐peak performance and this performance has been applied to the observer or residual generator design problems in many reports 14‐16 . The peak‐to‐peak residual generator design aims to minimize the worst‐case peak value of the residuals concerning peak bounded uncertainties.…”