Robust stochastic tracking for discrete-time models: designing of ellipsoid where random trajectories converge with probability one

We study the behaviour 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 ‘averaged’ ellipsoid in the tracking-error space where all system's trajectories arrive ‘with probability one’. The selection of the ‘best’ gain matrices is realised numerically by application of the robust attractive ellipsoid method with the linear matrix inequality technique application. The suggested approach is illustrated by designing of a robust tracking controller for a benchmark example in the presence of stochastic noises both in the state dynamics and in the output observations.