Robust Stability Criterion for State-Delayed Discrete-Time Systems Combined with a Saturation Operator on the State-Space

The problem of global asymptotic stability (GAS) of fixed-point state-delayed uncertain discrete-time systems combined with a saturation operator in state-space is investigated in this paper. The uncertainties in the system are presumed to be norm-bounded, which has been frequently employed in robust control for uncertain systems. This paper proposes a new GAS criterion for the considered system. The saturation nonlinearities associated with the system, which operate exclusively in the linear region, are identified using a unique methodology. Such identification leads to an improved characterization of saturation nonlinearities involved in the system. The proposed criterion utilizes an upper bound of parameter uncertainties, an asymptotic bound on the system's states, and a precise characterization of saturation nonlinearities involving system parameters. The merit of the criterion is also exemplified through examples along with simulation results.