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Computation of peak output for inputs satisfying many bounding conditions on magnitude and slope

The evaluation of peak outputs is an essential component of control systems design in which the outputs are required to remain within their prescribed bounds in the presence of all possible inputs. Characterising a possible set with many bounding conditions can reduce conservatism, thereby yielding a better design. However, this gives rise to difficulty in computing the peak outputs using analytical techniques. This article develops a practical method for computing the peak outputs of linear time-invariant systems for a class of possible sets characterised with many bounding conditions on the two- and/or the infinity-norms of the inputs and their slopes. The original infinite-dimensional convex optimisation problem is approximated as a large-scale convex programme defined in a Euclidean space with sparse matrices, which can be solved efficiently in practice. A case study of control design for a building subject to seismic disturbances is reinvestigated, where three bounding conditions are used. The numerical results show that the design so obtained is better than the previous one.