Identifi ability and Detectability of Lyapunov Exponents for Linear Dynamical Systems

Abstract

Lyapunov exponents (LE) are an effective tool for analyzing the qualitative characteristics of dynamic systems. Identifiability, recoverability and detectability problem of Lyapunov exponents not studied. This problem is actual. We propose an approach for verifying identifiability, recoverability and detectability. The approach bases on the analysis of geometric frameworks depending on the structural properties coefficient of the system. The structural properties coefficient reflects the change in Lyapunov exponents, and geometric frameworks are a source for deciding on the type of indicators. We obtain conditions for the complete detectability of Lyapunov exponents. These conditions guarantee the receipt of indicators set. We propose a criterion of σ-detectability with a level of υ-non-recoverability and give a method to evaluate it. We propose the method for verifying the adequacy of the Lyapunov exponents set. The permissible mobility border of the largest Lyapunov exponent obtains.