A novel LMI-based optimization algorithm for the guaranteed estimation of the domain of attraction using rational Lyapunov functions

Stability and robust design using a sector nonlinearity approach for nonlinear manufacturing systems

“…While these methods can obviously guarantee stability at the operating point, they cannot ensure stability in the whole state domain. A suitable stability domain will be crucial to the robust performance of the nonlinear dynamic system [18,19], as shown in Fig. 1.…”

“…This design simultaneously considers influences from both the nonlinear term and parameter variations, where two objective functions C 1 in (19) and C 2 in (23) are integrated into a unified objective function using the weighted-sum method:…”

“…All of these design methods have had many successful applications for linear or weakly nonlinear systems. However, they may not work well for a strongly nonlinear system, because the stability designed at the operation point may not work well in other locations due to the nonlinear characteristics [18,19]. Moreover, a good design should have the minimum sensitivity of the system eigenvalues to parameter variations.…”

A fast sampling method for estimating the domain of attraction

“…Although Lyapunov-based techniques have been successfully implemented for estimating the DoAs of various nonlinear systems [8], there are still two main issues with using these approaches. The first is that most of the existing methods are limited to polynomial systems [12,31]. As such, in the case of nonpolynomial systems, first, the equations of motion are approximated by using the Taylor's expansion and then the DoA is computed based on the approximated polynomial equations.…”

The Domain of Attraction for a Seir Epidemic Model Based on Sum of Square Optimization

“…As a result, many scholars paid more attention to some optimization problems, in order to estimate DOA, both qualitatively and quantitatively. An algorithm for solving the optimization problems for estimation of DOA via the approach employing LMI techniques is found in Hachicho and Tibken [5,4]. Matallana [15] gave a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions.…”