Lyapunov-based Methods for Maximizing the Domain of Attraction

Abstract

This paper investigates Lyapunov approaches to expand the domain of attraction (DA) of nonlinear autonomous models. These techniques had been examined for creating generic numerical procedures centred on the search of rational and quadratic Lyapunov functions. The outcomes are derived from all investigated methods: the method of estimation via Threshold Accepted Algorithm (TAA), the method of estimation via a Zubov technique and the method of estimation via a linear matrix inequality (LMI) optimization and genetic algorithms (GA). These methods are effective for a large group of nonlinear models, they have a significant ability of improvement of the attraction domain area and they are distinguished by an apparent propriety of direct application for compact and nonlinear models of high degree. The validity and the effectiveness of the examined techniques are established based on a simulation case analysis. The effectiveness of the presented methods is evaluated and discussed through the study of the renowned Van der Pol model.

Nonlinear Analysis of a Quasi-Zero Stiffness Air Suspension Based on the Cell-Mapping Method

“…The different initial pressures p and the initial positions d of the actuator piston are selected to study the stability and suspension performance. 18,19 When t ≤ 0, that is, p ≤ 4, it can be seen from the above judgment that (0, 0) is a stable point. If d = 0.1, there is only one equilibrium point (x, y) = (0, 0) and it is a stable equilibrium point.…”

“…Qualitative and quantitative research on this class of nonlinear vibration differential equations, including equilibrium stability and equilibrium attraction domain, has practical significance for the stability and safety in the actual use of this kind of suspension. 18…”

Evaluating the maximum domain of parameter model uncertainties in the combustion of a Diesel engine

“…The problem of interest is to find the maximum values of the scalars γA and γB so that the closed-loop system defined by ( 9), (10) remains stable given the optimal command in (7) [10], [16].…”

Design of a Fuzzy Optimization Control Structure for Nonlinear Systems: A Disturbance-Rejection Method

“…Uncertainties, such as un-modeled or unknown dynamics, process parameter variations and external disturbances appear in the built models [10] and influence the performance. Consequently, the design of control systems is significantly affected when the disturbance is attenuated [11][12][13][14]. As a result, control algorithms created based on disturbance observers have been formulated to neutralize such uncertainties [15][16][17][18].…”