Comparative study of methods for computing the maximal output for the design of critical systems

Computing the maximal output of a linear time-invariant (LTI) system is an important part of the design of critical systems. We compare three numerical methods for computing the maximal output of an LTI system subject to inputs with limited magnitude and rate of change. The three methods are: (1) quadratic programming method, (2) convex optimisation method, and (3) upper bound method. Two numerical examples are given to examine the three methods in terms of accuracy, efficiency, and conservativeness. We show that the quadratic programming method is superior to the other two methods from the viewpoint of accuracy and efficiency of computing the theoretically maximal output, while only the convex optimisation method has the capability to allow for the input´s frequency range, which leads to good estimation of the practically maximal output and less conservative control system design. We also issue a guideline for selecting the order of Fourier series expansion required in the convex optimisation method