Sensitivity reduction in modal control systems

The conventional modal control theory is concerned with the problem of determining a state feedback matrix-valued gain which drives the system eigenvalues to prescribed positions. When the parameters of the open-loop system involve certain variations, the closed-loop eigenvalues, obtained by using a feedback gain determined as above, also contain variations. In the present paper the problem of choosing an additional state feedback gain such as to reduce the closed-loop eigenvalue variations as much as desired is solved. Specifically, upon the assumption that a nominal set of parameter values is given, and that a feedback modal control law which drives the eigenvalues of the nominal closed-loop system to the desired positions is known, two alternative expressions for the required additional reduced eigenvalue sensitivity feedback controller are derived. Both cases of known and unknown system state vector are considered. The theory is illustrated by several examples.