On Computing the Worst-Case Norm of Convolution Systems: A Comparison of Continuous-time and Discrete-time Approaches

This paper compares two approaches to compute the worst-case norm of finite-dimensional convolution systems. All admissible inputs are defined to have bounded magnitude and limited rate of change. Due to physical and mathematical reasons, the inputs are also specified to start from zero. The first approach is based on continuous-time optimal control formulation. Necessary conditions obtained via the Pontryagin's maximum principle provide a systematic means to characterize and construct the worst-case input. The second approach is based on discretization of the norm-computation problem which results in a large-scale finite-dimensional linear programming. We also investigate computational errors including truncation errors and discretization errors. Although the second approach seems to be simpler, the first approach is deemed to yield better accuracy.