Stochastic stability of a recoverable computer control system modeled as a finite-state machine

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 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 discrete-time jump-linear dynamical system. It is shown in some detail how such a model can be used to characterize rollback recovery algorithms. A specific example is given where mean-square stability is determined as a function of upset persistency and various algorithm parameters.