Integral control of linear systems with actuator nonlinearities: lower bounds for the maximal regulating gain

Closing the loop around an exponentially stable single-input single-output regular linear system, subject to a globally Lipschitz and non-decreasing actuator nonlin-earity and compensated by an integral controller, is known to ensure asymptotic tracking of constant reference signals, provided that (a) the steady-state gain of the linear part of the plant is positive, (b) the positive integrator gain is suuciently small and (c) the reference value is feasible in a very natural sense. Here we derive lower bounds for the maximal regulating gain for various special cases including systems with non-overshooting step-response and second-order systems with a time-delay in the input or output. The lower bounds are given in terms of open-loop frequency/step response data and the Lip-schitz constant of the nonlinearity, and are hence readily obtainable.