Abstract: To address the lack of a systematic state-space model, stability analysis, and parameter co-tuning method for the incremental proportional-integral-derivative-proportional (PID-P) structure in cascade control systems, we propose a novel co-design approach for the incremental PID-P controller. First, we establish a discrete-time state-space model of the incremental PID-P structure. Second, by constructing a new Lyapunov function and leveraging stability theory, we derive sufficient conditions for the closed-loop system stability, along with a co-tuning strategy that simultaneously determines all gain parameters of both primary and secondary controllers. Finally, we conduct simulation verification on the main steam temperature control system of a thermal power plant. The results demonstrate that, compared to the traditional positional proportional-integral (PI) controller, the proposed method reduces the settling time by 36.6%, achieves smaller overshoot, and ensures faster convergence. Additionally, when compared to the incremental PID controller based on linear quadratic regulator theory, the proposed method exhibits superior performance in terms of state norm peak, settling time, and integral error criteria (ISE/IAE). Moreover, the system maintains favorable dynamic performance and robust stability even under input disturbances and parameter perturbations. Simulation results validate the effectiveness of the proposed method in enhancing dynamic response speed, transient performance, and robustness.