Observer-based stabilization of one-sided Lipschitz systems with application to flexible link manipulator

Abstract

This article is concerned with the observer-based output feedback stabilization problem for a class of nonlinear systems that satisfies the one-sided Lipschitz and the quadratically inner-bounded conditions. The system model under consideration encompasses the classical Lipschitz nonlinear system as a special case. For such a system, we design the output feedback controller via constructing a full-order Luenberger-type state observer. Sufficient conditions that guarantee the existence of observer-based output feedback are established in the form of linear matrix inequalities, which are readily solved by the available numerical software. Moreover, the proposed observer-based output feedback designs are applied to a flexible link manipulator system. Finally, simulation study on the manipulator system is given to demonstrate the effectiveness of the developed control design.

Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities

“…Noting that the quadratically inner‐bounded property is the promotion of the Lipschitz and one‐sided Lipschitz property, different from that the Lipschitz constant must be positive, θ 1 i and θ 2 i can be a positive number, a negative number, or zero. Meanwhile, quadratically inner‐bounded nonlinearity only needs to satisfy one of the two conditions of the one‐sided Lipschitz property; thus, the system with quadratically inner‐bounded nonlinearity discussed in this paper is less conservative than the existing results about Lipschitz or one‐sided Lipschitz nonlinearities, and more properties of quadratically inner‐bounded nonlinearities can be found in the works of Wu et al and Benallouch et al To our best knowledge, few articles discuss this kind of nonlinear terms.…”

“…Other works discussed the system with Lipschitz nonlinearities. It is worth noting that the one‐sided Lipschitz condition has been frequently used in the study of synchronization of complex networks; the works of Wu et al and Benallouch et al considered systems with one‐sided Lipschitz nonlinearities. The class of nonlinearities considered in this paper is fairly general.…”

“…"> 1.Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities is firstly investigated in this paper. Compared to systems with Lipschitz or one‐sided Lipschitz nonlinearities addressed in other works, quadratically inner‐bounded nonlinearities discussed in this paper are more general. 2.The conditions proposed not only ensure that the closed‐loop system is regular, causal, and uniformly finite‐time bounded (UFTB) but also guarantee the existence and uniqueness of solution for the system.…”

“…Moreover, it is well known that almost all the systems in our life are inevitably nonlinear. Therefore, a lot of works have been done on nonlinear systems, including nonlinear switched systems and nonlinear Markov jump systems . However, most of the nonlinearities considered in these papers are Lipschitz or one‐sided Lipschitz.…”

“…Manivannan and Muralisankar discussed the stability analysis of Lipschitz nonlinear switched singular systems with the ADT approach based on LMI and the delay decomposition approach. Wang et al discussed the finite‐time stabilization for Lipschitz nonlinear discrete‐time singular Markov jump systems with the ADT approach, and in another work of Wang et al, the stability and stabilization for Lipschitz nonlinear continuous‐time descriptor semi‐Markov jump systems were of concern; the existence and uniqueness of solution was simultaneously considered in other works of Wang et al On the basis of the observer, Kheloufi et al discussed robust stabilization for systems with Lipschitz nonlinearities, and Wu et al considered the stabilization problem for one‐sided Lipschitz systems. However, quadratically inner‐bounded nonlinearities are more general than Lipschitz or one‐sided Lipschitz ones; different from the Lipschitz constant being a positive number, the parameters of the quadratically inner‐bounded property can be positive, negative, or zero.…”