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Most of the practical systems including aircraft system dynamics are nonlinear and stochastic in nature, so the linearized models without having accurate knowledge of noise characteristics to them may lead to inaccurate results and poor performance. In the presence of measurement & process noise, the parameters estimates of dynamic systems are asymptotically biased, inconsistent and inefficient. In the case of state estimation of nonlinear system, researchers have been proposed to design observers using Lyapunov theory based stability analysis. The selection of Lyapunov function is not easy in practice as it does not have specific guidelines for such selection. Contraction theory is an alternative approach to visualize the stability results for nonlinear system, & exploits the incremental behavior of the trajectories of a system with respect to each other. The stability analysis using contraction theory eliminates the selection of Lyapunov function and its extension to stochastic nonlinear system is an active research area. This book is focused on system identification of aircraft system from noisy data, and stability analysis of aircraft system in stochastic contraction framework.