The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem.
We give an approach to large deviation type asymptotic problems without evident probabilistic representation behind. An example provided by the mean field models of quantum statistical mechanics is considered.
An interesting analogy can be found between recognition of noisy, distorted, or incomplete structural patterns and analysis, modelling and control of actual discrete event systems, where different types of uncertainty can occur.