Design of nonlinear feedback systems with inputs and outputs satisfying bounding conditions

This paper develops a method for designing a feedback system comprising a static memoryless nonlinearity and linear time-invariant convolution subsystems so as to ensure that the error and the controller output stay within prescribed bounds for all time and for all inputs having bounded magnitude and bounded slope. Since the original design criteria are computationally intractable, we derive practical sufficient conditions for ensuring them. The conditions provide surrogate design criteria that are in keeping with the method of inequalities. Essentially, the nonlinearity is replaced with a fixed gain and an equivalent disturbance; thus, the nominal system used during the design process becomes linear and the associated performance measures are readily obtainable by known methods. To illustrate the usefulness of the method, a design example of a hydraulic force control system is given.