A PRIORI BOUNDS ON THE PERFORMANCE OF

The problem of bounding the optimal cost of nonlinear dynamical sys-tems is studied. Conditions are given under which it is possible to upper bound the optimal performance of a nonlinear system with a quadratic cost functional by the optimal performance of a linear sys-tem with the same cost functional. Results are stated both in the fre-quency and the time domain. A sharp lower bound for the optimal performance of a linear system with quadratic penalty function is given in terms of the performance of a class of suboptimal systems. The application of this result to direct evaluation of the degree of suboptimality of a given design is studied. Two numerical examples illustrate the usefulness of the results in design procedures whe