Robust poles assignment for a kind of second-order linear time-varying systems

In this paper, we focus on a class of second-order linear time-varying(LTV) systems in which the control input matrices is invertible, a time-varying controller design method is presented to arbitrarily place the closed-loop poles at fixed locations for these systems. The desired fixed poles can ensure the stability of the closed-loop systems. Furthermore, these poles can also ensure good response performances of the closed-loop systems, unlike other poles placement methods for LTV systems. To improve the robustness with respect to the uncertainties of system coefficient matrices, an optimization problem for the design freedoms of the controller is solved. For the sake of use in practical applications, a design problem for the attitude control of the spacecrafts with time-varying moment of inertia is investigated. The simulation results verify the effectiveness of the proposed robust design approach.