Axiomatic Foundations of Anisotropy-Based and Spectral Entropy Analysis: A Comparative Study

An axiomatic development of control systems theory can systematize important concepts. The current research article is dedicated to the investigation and comparison of two axiomatic approaches to the analysis of discrete linear time-invariant systems affected by external random disturbances. The main goal of this paper is to explore axiomatics of an anisotropy-based theory in comparison with axiomatics of a spectral entropy approach in detail. It is demonstrated that the use of the spectral entropy approach is mathematically rigorous, which allows one to prove that the minimal disturbance attenuation level in terms of an anisotropy-based control theory provides the desired performance that is not only for ergodic signals. As a result, axiomatics of the spectral entropy approach allows one to rigorously prove that anisotropy-based controllers can be used to guarantee the desired disturbance attenuation level, not only for stationary random sequences, but also for a wider set of input random signals.

Automated summary

An axiomatic development of control systems theory can systematize important concepts. The current research article investigates and compares two axiomatic approaches for analyzing discrete linear time-invariant systems affected by external random disturbances. The main goal of the paper is to explore and compare the anisotropy-based theory with the spectral entropy approach. The spectral entropy approach is shown to be mathematically rigorous and it proves that anisotropy-based controllers can guarantee the desired disturbance attenuation level for a wider set of input random signals.