Parametric State Feedback Control with Response Insensitivity

A recent parameterization of the class of linear feedback controllers which assign a set of desired self-conjugate eigenvalues to the closed-loop system is used to formulate and solve a fundamental response insensitivity problem. It is established to what extent state feedback control can be used to render the closed-loop system response insensitive to possibly many not necessarily small parameter variations in the open-loop state-space model. A nonconservative sequential design procedure is developed for making as many of the closed-loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed-loop eigenvalues. The main result is a class of desensitizing fixed gain state feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements.