Low‐gain integral control for a class of discrete‐time Lur'e systems with applications to sampled‐data control

We 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

Adaptive Low-Gain Integral Control of Linear Systems with Input and Output Nonlinearities

An adaptive low-gain integral control framework is developed for tracking constant reference signals in a context of finite-dimensional, asymptotically stable, single-input, single-output linear systems subject to locally Lipschitz, monotone input and output nonlinearities of a general nature: the input nonlinearity is required to satisfy an asymptotic growth condition (of sufficient generality to accommodate nonlinearities ranging from saturation to exponential growth) and the output nonlinearity is required to satisfy a sector constraint in those cases wherein the input nonlinearity is unbounded