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SOSTOOLS Version 3.00 Sum of Squares Optimization Toolbox for MATLAB
TLDR
SOSTOOLS v3.00 is the latest release of the freely available MATLAB toolbox for formulating and solving sum of squares (SOS) optimization problems. Expand
Region of Attraction Estimation Using Invariant Sets and Rational Lyapunov Functions
TLDR
This work addresses the problem of estimating the region of attraction (RA) of equilibrium points of nonlinear dynamical systems and provides an algorithm that is guaranteed to enlarge the estimate of the RA at each iteration. Expand
A Decomposition Technique for Nonlinear Dynamical System Analysis
TLDR
A method for analyzing large-scale nonlinear dynamical systems by decomposing them into coupled lower order subsystems that are sufficiently simple for computational analysis is presented. Expand
Tuning the dials of Synthetic Biology
Synthetic Biology is the ‘Engineering of Biology’ – it aims to use a forward-engineering design cycle based on specifications, modelling, analysis, experimental implementation, testing and validationExpand
Model decomposition and reduction tools for large-scale networks in systems biology
TLDR
Biological system models are routinely developed in modern systems biology research following appropriate modelling/experiment design cycles. Expand
Robust nonlinear stability and performance analysis of an F/A‐18 aircraft model using sum of squares programming
SUMMARY In this paper, we develop algorithms for the computational analysis of stability and robust performance properties of nonlinear models governed by polynomial differential equations inExpand
On validation and invalidation of biological models
TLDR
We develop different approaches for showing how competing ordinary differential equation (ODE) based models of the same biological phenomenon containing nonlinearities and parametric uncertainty can be invalidated using experimental data. Expand
Advances in computational Lyapunov analysis using sum-of-squares programming
The stability of an equilibrium point of a nonlinear dynamical system is typically determined using Lyapunov theory. This requires the construction of an energy-like function, termed a LyapunovExpand
Sum of Squares Optimization Toolbox for MATLAB User ’ s guide Version 2 . 00 June 1 , 2004
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of theExpand
Region of attraction analysis via invariant sets
TLDR
In this work we address the problem of estimating the region of attraction (RA) of a nonlinear dynamical system governed by polynomial vector fields and semi-algebraic sets and provide an algorithm that with each iteration is guaranteed to enlarge the estimate of the RA. Expand
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