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In this work we address the problem of estimating the region of attraction (RA) of a nonlinear dynamical system. We propose a method that uses a Lyapunov type approach to obtain an estimate of the RA, however, the obtained invariant sets are not level sets of the Lyapunov function certificates. We then restrict our attention to systems governed by polynomial vector fields and semi-algebraic sets and...
We introduce a method for analyzing large-scale power systems by decomposing them into coupled lower order subsystems. This reduces the computational complexity of the analysis and enables us to scale the Sum of Squares programming framework for nonlinear system analysis. The method constructs subsystem Lyapunov functions which are used to estimate the region of attraction pertaining to the equilibrium...
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. It is shown that the decomposition approach can be used to scale the Sum of Squares programming framework for nonlinear systems analysis. The method constructs subsystem Lyapunov functions which are used to form...
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