Open AccessState-feedback anisotropy-based robust control of linear systems with polytopic uncertainties
Author(s) -
Alexey A. Belov
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1536/1/012008
Subject(s) - control theory (sociology) , mathematics , norm (philosophy) , linear matrix inequality , anisotropy , signal (programming language) , disturbance (geology) , state (computer science) , linear system , computer science , mathematical optimization , control (management) , algorithm , law , physics , mathematical analysis , quantum mechanics , political science , biology , paleontology , artificial intelligence , programming language
In this paper, linear discrete-time systems with polytopic uncertainties affected by random external disturbances are under consideration. The input disturbance is supposed to be a stochastic signal with known mean anisotropy, which stands for a spectral color of the signal. The anisotropic norm of the system indicates its stochastic gain from the input disturbance with the same mean anisotropy level to the output of the system. The problem is to find state-feedback control law that robustly stabilizes the uncertain system and guarantees desired performance index subject to input disturbance for all possible uncertainties. In order to solve this problem, Lyapunov functions technique and matrix inequalities approach are used to obtain the numerically effective procedure. To illustrate the efficiency of the proposed conditions, a numerical example is considered.