Determining exact maximum amplitude limit cycles in digital filters

It is shown that the problem of determining the maximum amplitude limit cycle of a given period in a second order digital filter can be formulated as an integer linear program. Unfortunately, for even moderate limit cycle periods, the ILP can require considerable CPU time. A more straightforward procedure is thus proposed, which considers all possible initial states, which can be a maximum amplitude state of a limit cycle. Results are presented which significantly reduce the number of states requiring consideration, thereby resulting in a computationally feasible algorithm.