Finite-Time Convergence Stability of Lur’e Discrete-Time Systems

Abstract

Abstract:In this paper, a constructive design methodology for Finite-Time Stability (FTS) of a class of nonlinear discrete-time systems is proposed. A dead-beat controller that can achieve n-finite-time stability is constructed. Furthermore, stability conditions, based on the use of Borne and Gentina practical stability criterion and matrices in the Benrejeb arrow form, are synthesized. Similarity between transient behaviors of dead-beat controlled linearized and nonlinear third order systems are shown and concluding remarks are formulated.

On the Sampling and the Performance Comparison of Controlled LTI Systems

“…Moreover, it was observed that under some matching conditions, the dead-beat controller based on the Tustin approximation leads to an n-finite-time stabilization of the exact sampled-data n order system. Developed results can be extended to finite-time stabilization of nonlinear systems as shown in [23].…”

“…This note investigates the influence of the discretization method in the controlled system properties. The work is a continuation of the previous paper [23] in which the effects of a ZOH discretization on the stability and stabilization properties of linear and nonlinear Lure-type systems are considered. The aim of this paper is to investigate more discretization techniques, mainly, the forward Euler and the Tustin approximations, and study the impact of a numerical approximation on the control system (5) on the system properties in term of stability and finite-time stability.…”

“…The discussion is based on an example of a third order system that, from our point of view, can be understood in a common framework to select discrete-time models and synthesize dead-beat controllers. The treatment is limited for simplicity to the linear case but the extension to the www.ijacsa.thesai.org nonlinear case is possible, at least for some class of Lure-type systems, by considering sector bounded nonlinearities [23].…”