A complete stability analysis for planar delta operator systems subject to state saturation

In this paper, stability analysis is investigated for planar delta operator systems subject to state saturation. General properties of limit trajectories are characterized for the planar delta operator systems subject to state saturation. A nontrivial limit trajectory only intersects with two pairs of opposite sides but not neighboring sides of a unit square. Hence, a relation is established between the present intersection of a trajectory with lines x₂ = ±1 and the next intersection. Necessary and sufficient conditions on global asymptotic stability are obtained for the planar delta operator systems with full and partial saturated state. Simulation results are given to show the effectiveness of the proposed methods.