The Chebyshev norm as a deterministic alternative for problems with uncertainties

The problem of determining, for a dynamic system, the absolute optimum response characteristics when portions of the system are not fully prescribed, and the best and worst possible performance when the excitation is uncertain is formulated as a mathematical programming problem with equality and inequality constraints. The objective is to extremize the maximum time value of a response, i.e. a Chebyshev norm is employed. A linear example problem and its solution are presented to illustrate the formulation.