In this chapter, a system solution-based direct method combined with auxiliary model is proposed to investigate global exponential stability criteria of the zero equilibrium point for a kind of discrete-time HOCGNNs with time-varying connection weights, delays, and impulses. First, an impulse-free discrete-time HOCGNN with time-varying connection weights and delays is constructed, and the relationship between the solutions of original and new discrete-time HOCGNNs is presented. Then, a system solution-based direct method is proposed to investigate global exponential stability criteria for the zero equilibrium point of impulse-free discrete-time HOCGNNs. From which, global exponential stability criteria for the zero equilibrium point of original discrete-time HOCGNNs are derived. Finally, the effectivity of the obtained global exponential stability criteria is explained via numerical examples.