arXiv:2611.13153v1 Announce Type: new Abstract: Intelligent proportional (iP) controllers, introduced in the framework of model-free control, are often presented as an alternative to proportional-integral (PI) controllers that requires no model of the plant. This paper studies this property for a first-order linear plant under sampled-data implementation with a zero-order hold. When the time derivative of the output is estimated by a backward difference, the discrete-time iP and PI controllers are known to obey the same control law under a one-to-one correspondence between their parameters. Building on this correspondence, the paper derives necessary and sufficient conditions for exponential stability of the iP closed loop, in closed form, in terms of the controller parameters KP and alpha, the sampling period h, and the plant parameters. It then shows that, when the iP parameters are held fixed and the sampling period tends to zero, the closed-loop decay rate tends to the iP gain KP, provided that KP is positive and that the ratio rho between the input gain of the plant and alpha satisfies 0 < rho < 2. One closed-loop pole then behaves as 1 - h KP, while the other tends to 1 - rho. With fixed PI gains, by contrast, the decay rate tends to that of the continuous-time PI loop, which depends on the plant parameters. The two parametrizations therefore suggest different tuning procedures, although they achieve the same closed loops at every fixed sampling period. High gain for the PI is, in some sense, replaced by fast sampling of the iP. The results also make explicit which plant information the iP controller requires: the sign of the input gain and a bound on its magnitude in the limit of fast sampling, and bounds on both plant parameters at a given sampling period. Numerical experiments illustrate these results.