Bounded H∞-control for non-linear discrete-time uncertain systems

Discrete-time affine control systems with parameter uncertainty and exogenous disturbances are considered in the paper. Such systems are examined, where there is an a priori constraint on the Euclidean norm of the control. The nominal free system is supposed to be exponentially stable, the parameter uncertainty is cone-bounded. A saturation type state-feedback control is proposed. A sufficient condition is formulated, which assures that the proposed state-feedback control is an H_∞-control with an appropriately chosen bound of the L₂-gain. A numerical example illustrates the results.