Robust control with pole shifting via performance index modification

Robust controllers that ensure closed-loop eigenvalue placement are designed for linear systems with parametric uncertainties. By using an appropriate state weighting matrix choice and a relative stability degree, an LMI-based algorithm is proposed to provide guaranteed cost controllers that ensure (i) the closed-loop nominal eigenvalues shifting by a pre-specified amount (ii) a prescribed degree of stability for all system uncertainties of a given class. A certain level of closed-loop performance is also ensured by minimizing the associated guaranteed cost.