Random Disturbance Attenuation in Discrete-time Polytopic Systems: Performance Analysis and State-Feedback Control

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 random sequence 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 aim of the paper is to derive numerical procedures to analysis and state-feedback control of linear discrete systems with polytopic uncertainties using anisotropy-based performance criterion. The analysis problem is to check robust stability and performance index of the uncertain system with respect to random input disturbances with known mean anisotropy level. The control problem is to find state-feedback gain that robustly stabilizes the uncertain system and guarantees desired anisotropy-based performance index for all possible uncertainties. In order to solve this problem matrix inequalities approach is used to obtain the numerically effective procedure. To illustrate the efficiency of the proposed conditions, a numerical example is considered.