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Recently sum-of-squares (SOS) based methods have been used for the stabilityanalysis and control synthesis of polynomial dynamical systems. This analysisframework was also extended to non-polynomial dynamical systems, includingpower systems, using an algebraic reformulation technique that recasts thesystem's dynamics into a set of polynomial differential algebraic equations.Nevertheless, for large scale dynamical systems this method becomesinapplicable due to its computational complexity. For this reason we develop asubsystem based stability analysis approach using vector Lyapunov functions andintroduce a parallel and scalable algorithm to infer the stability of theinterconnected system with the help of the subsystem Lyapunov functions.Furthermore, we design adaptive and distributed control laws that guaranteeasymptotic stability under a given external disturbance. Finally, we apply thisalgorithm for the stability analysis and control synthesis of a networkpreserving power system.

Stability and Control of Power Systems using Vector Lyapunov Functions and Sum-of-Squares Methods