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In this study, we develop algorithms for robust estimation and fault detection and identification for a class of hybrid systems called the stochastic linear hybrid system (SLHS). The authors propose a robust hybrid estimation algorithm that estimates the continuous state and the discrete state of an SLHS with unknown fault inputs. The algorithm decouples the unknown fault input from the estimation error dynamics for each discrete state of the hybrid system to guarantee the convergence of the estimation error. The robust hybrid estimation algorithm is designed for two kinds of discrete state transition models: the Markov-jump transition model whose discrete transition probabilities are constant (i.e. independent of the continuous state) and the state-dependent transition model whose discrete state transitions are determined by some guard conditions (i.e. dependent on the continuous state). The proposed residual generation algorithm computes residuals to facilitate fault detection and isolation. The residuals have the properties that they can reconstruct (in the mean sense) the unknown fault input vector. The authors also demonstrate the performance of the proposed algorithm with a vertical take-off and landing aircraft example.