Probabilistic analysis of Robust Attractive Ellipsoids for quasi-linear discrete-time models

We study the behavior of stochastic discrete-time models controlled by an output linear feedback during a tracking process. The controlled system is assumed to be nonlinear satisfying the global “quasi-Lipschitz” condition and subjected to stochastic input and output disturbances. Two gain matrices (in a feedback and in an observer) define an ellipsoid in the tracking-error space where all system´s trajectories arrive “with probability one”. The selection of the “best” gain matrices is realized numerically by application of the Robust Attractive Ellipsoid Method (RAEM) with the Linear Matrix Inequality (LMI) technique application.