Affiliation:
1. V.A. Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia
Abstract
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.
Funder
Russian Science Foundation
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference30 articles.
1. Axiomatic foundation of the theory of control systems;Roxin;IFAC Proc. Vol.,1963
2. Systems Theory as the Foundation for Understanding Systems;Adams;Syst. Eng.,2014
3. Axiomatic Design Theory for Systems;Suh;Res. Eng. Des.,1998
4. Yoong, C., Palleti, V., Maiti, R., Silva, A., and Poskitt, C. (2021). Deriving invariant checkers for critical infrastructure using axiomatic design principles. Cybersecurity, 4.
5. Semyonov, A., Vladimirov, I., and Kurdyukov, A. (1994, January 14–16). Stochastic approach to H∞-optimization. Proceedings of the 1994 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, USA.