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Stability analysis tools are essential to understanding and controlling anyengineering system. Recently sum-of-squares (SOS) based methods have been usedto compute Lyapunov based estimates for the region-of-attraction (ROA) ofpolynomial dynamical systems. But for a real-life large scale dynamical systemthis method becomes inapplicable because of growing computational burden. Insuch a case, it is important to develop a subsystem based stability analysisapproach which is the focus of the work presented here. A parallel and scalablealgorithm is used to infer stability of an interconnected system, with the helpof the subsystem Lyapunov functions. Locally computable control laws areproposed to guarantee asymptotic stability under a given disturbance.

A Sum-of-Squares approach to the Stability and Control of Interconnected Systems using Vector Lyapunov Functions