A computational capability for the evaluation of the limiting performance of transient dynamic systems is described. This capability permits the peak response (acceleration, force, displacement, or stress) of a system to be computed if portions of the system are optimally controlled or isolated. Thus, the worst occurrence to a human or vehicle can be determined under prescribed impact conditions if restraints such as seat belts or bumpers were to react in a time-optimal fashion and if response constraints on the system were not violated. No design configurations of the controllers or isolators are specified. Several specific applications of the capability to human and transportation systems are presented. In terms of design, this capability allows the designer to ascertain on the basis of response specifications alone the feasibility of a proposed design; in addition, he can measure and monitor his success during the design process. This is possible because the capability provides characteristics of the theoretically best, i.e., the limiting, design concept. Without the characteristics of the limiting design, the evaluation of proposed designs can be made only by performing a multitude of analyses for each candidate design. The problem is formulated in terms of linear programming. The controllers can be nonlinear, linear, active, or passive, while the remainder of the system must be linear. The linear programming formulation permits the use of off-the-shelf computer programs for the solution and, because of the capability of standard linear programs, means that multidegree-of-freedom, multi-isolator problems subjected to multiple, alternative sets of transient loading can be treated.