Abstract
AbstractWe study low‐gain (P)roportional (I)ntegral control of multivariate discrete‐time, forced Lur'e systems to solve the output‐tracking problem for constant reference signals. We formulate an incremental sector condition which is sufficient for a usual linear low‐gain PI controller to achieve exponential disturbance‐to‐state and disturbance‐to‐tracking‐error stability in closed‐loop, for all sufficiently small integrator gains. Output tracking is achieved in the absence of exogenous disturbance (noise) terms. Our line of argument invokes a recent circle criterion for exponential incremental input‐to‐state stability. The discrete‐time theory facilitates a similar result for a continuous‐time forced Lur'e system in feedback with sampled‐data low‐gain integral control. The theory is illustrated by two examples.
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