Parametric state-feedback control for arbitrary eigenvalue assignment with minimum sensitivity

The problem of closed-loop system eigenvalue sensitivity to small parameter variations in some, but not all, of the elements of the open-loop system model matrices is considered. An insightful parameterisation of all assignable closed-loop eigenvalue sensitivities is provided through the application of a recent explicit parameterisation of the class of linear eigenvalue-assigning state-feedback controllers. Based on this parameterisation, a numerical optimisation method for designing a constant gain feedback matrix which assigns the closed-loop eigenvalues to desired locations, such that these eigenvalues have low sensitivity to variation in the open-loop state-space model, is presented.