Output Feedback in the Design of Eigenstructures for Enhanced Sensitivity

The problem of closed-loop enhanced sensitivity design is as follows: given a linear, time-invariant system, find a (realizable) feedback gain such that (1) the closed-loop is stable in the reference and the potentially damaged states, and (2) the eigenstructure includes a subset of poles, with desirable derivatives, that lie in a part of the plane where identification is feasible. For state feedback the eigenstructure is typically assignable and stability in the reference state is easily enforced. For output feedback, however, only partial assignment is possible, and it is here shown that the standard SVD design scheme leads to generically unstable eigenstructures when measurands are homogeneous (that is, when all sensors measure displacements, velocities, or accelerations). The mechanics that govern this behavior are clarified and a mitigating strategy that retains the convenience of homogeneous sensing is offered.