Bounds on the state vector growth rate in stochastic dynamical systems

A stochastic dynamical system represented through a linear vector equation in idempotent algebra is considered. We propose simple bounds on the mean growth rate of the system state vector, and give an analysis of absolute error of a bound. As an illustration, numerical results of evaluation of the bounds for a test system are also presented.

💡 Research Summary

The paper investigates stochastic dynamical systems that are expressed in the framework of idempotent (max‑plus) algebra. In this setting a system evolves according to the linear vector recursion x(k + 1) = A(k) ⊗ x(k), where ⊗ denotes the max‑plus matrix‑vector product, x(k)∈ℝⁿ is the state vector at discrete time k, and A(k) is a random matrix whose entries are independent random variables. The principal performance metric of interest is the mean growth rate of the state vector, defined as λ = limₖ→∞ (1/k) E