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In this paper a modeling framework is introduced for describing how complex recovery algorithms used to implement safety critical control systems on a recoverable computer can affect the stability and performance characteristics of the closed-loop system. The model has a hybrid structure consisting of three distinct parts: a Markovian exosystem, a finite-state machine, and a jump-linear dynamical system. It is shown in some detail how such a model could be used to characterize rollback recovery algorithms. Two specific examples are given where mean-square stability is determined as a function of upset persistency and various algorithm parameters.