Robust tracking control for uncertain linear systems without matching conditions

In this paper, we consider a robust tracking problem for linear systems with time-varying uncertainties in both the state and the input matrices, where the matching condition of the uncertainties is not assumed. We address two cases of uncertainties: norm bounded uncertainties, and block-diagonally structured uncertainties. The conditions under which the tracking error is ultimately bounded and the closed loop stability is guaranteed for all allowable uncertainties, are proposed for the both cases of uncertainties, respectively. There are some free parameters to allow flexibility in determining the bound and the decaying rate of the tracking error. The robust tracking controllers are obtained by solving the linear matrix inequalities (LMI) which are equivalent to the suggested conditions. The bound and the decaying rate of the tracking error can be minimized and maximized via the corresponding LMI problems, respectively. The robust tracking property of the proposed controller is shown by an example