Stability analysis of stochastic systems using polynomial chaos

A novel framework for stability analysis of linear and polynomial stochastic systems is presented. The framework is built on generalized polynomial chaos theory, which enables analysis of dynamical systems with probabilistic uncertainty on system parameters with various distributions. The theory allows for the transformation of stochastic problems into a higher dimensional deterministic problem, that is able to accurately approximate the evolution of uncertainty in the state trajectories due to stochastic system parameters. The developed theory is applied to analyze a linear flight control design for an F-16 aircraft model. The problem of generating stability certificates for stochastic polynomial systems is also considered.