ON THE EFFECT OF WEAK NONLINEARITIES ON LINEAR CONTROLLABILITY AND OBSERVABILITY NORMS, AN INVARIANT MANIFOLD APPROACH

Many weakly non-linear structures exhibit normal modes that are analog ous to linear modes of linear oscillatory systems. As in the testing o f linear modal systems, optimal sensor and actuator placement is impor tant for obtaining the best test results. Such optimal placement is al so important in control. This paper addresses this issue by extending the concepts of modal controllability and observability norms develope d for linear systems to weakly non-linear systems that exhibit non-lin ear normal modes. (C) 1997 Academic Press Limited.