State-feedback anisotropy-based robust control of linear systems with polytopic uncertainties

Abstract

Abstract 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.