Evaluation of the Lyapunov Exponent for Stochastic Dynamical Systems with Event Synchronization

We consider stochastic dynamical systems operating under synchronization constraints on system events. The system dynamics is represented by a linear vector equation in an idempotent semiring through second-order state transition matrices with both random and constant entries. As the performance measure of interest, the Lyapunov exponent defined as the asymptotic mean growth rate of the system state vector is examined. For a particular system, we derive a general expression for the exponent under the assumptions that the random matrices are independent and identically distributed, and their random entries have finite means. To illustrate, the exponent is calculated in the case when the random entries have exponential and continuous uniform distributions. Key-Words: Stochastic dynamical system, Event synchronization, Idempotent semiring, Lyapunov exponent, Convergence in distribution