Output linear feedback tracking for discrete-time stochastic model using robust attractive ellipsoid method with LMI application

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 "in average". 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. The suggested approach is illustrated by designing of a robust tracking controller for a benchmark example in the presence of stochastic noises in the state dynamics as well as in the output observations.