An analytic solution for the state trajectories of a feedback control system

Abstract

In connection with the normal process of control system design, the determination of the state trajectories for the controlled system is frequently required. The procedure involved in the determination is straightforward. However, extensive computations may be needed, if either time-varying control gains are used, or if small integration step sizes are required by the presence of high-frequency system dynamics. The present investigation is concerned with an approach for overcoming the computational difficulties, taking into account a change of variables for the close-loop system dynamics equation. This procedure makes it possible to obtain a closed-form expression for the state trajectories.