Computation of Peak Output for Inputs Restricted in L₂ and L_∞ Norms Using Finite Difference Schemes and Convex Optimization

Control systems designed by the principle of matching gives rise to problems of evaluating the peak output This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two-and/or the infinity-norms of the inputs and their derivatives The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme deffned in a Euclidean space, which are associated with sparse matrices and thus can be solved effciently in practice The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.