Stabilization of unknown minimum-phase plant under Lipschitz uncertainty and bounded external disturbance

The paper addresses to problem of adaptive stabilization of unknown minimum-phase plant under Lipshitz uncertainty and bounded external disturbance. The nominal model of the plant is taken in the form of autoregressive moving average (ARMA) discrete-time system with unknown coefficients from a known bounded convex prior set. All the models from the prior set are minimum-phase, that is, input of any model is guaranteed to be bounded under bounded output. No upper bound on the external disturbance is assumed to be known to controller designer. Xie L.L. and Guo L. showed in 2000 that, in the case of the Lipshitz uncertainty that depends on the previous value of the output only, the particular value 3/2 + y/2 of the Lipshitz constant L is critical for the simplest dynamical plant: any plant with L > 3/2 + V2 can not be surely stabilized by any causal feedback while any plant with L