In this chapter, the problems of stability and stabilization via event-triggered state-feedback controllers are presented for two-dimensional (2-D) singular Roesser systems with directional time-varying delays. Based on a 2-D Lyapunov–Krasovskii functional (LKF) method, and by utilizing free matrix equations, delay-dependent conditions are first derived in terms of linear matrix inequalities (LMIs) to ensure the regularity, causality and internal stability of 2-D singular Roesser systems with time-varying delays. The derived stability conditions are then employed to derive tractable conditions for the design of a stabilizing event-triggered state-feedback controller (ETC). Numerical examples are given to illustrate the effectiveness of the proposed analysis and design conditions.