Trajectory stabilization for non-linear systems with non-lexicographically fixed linear approximate model

To stabilize some particular trajectory of general non-linear systems, it is a basic idea that the linear control technique is applied to an approximate linear model around the trajectory. However, since this model becomes a time-varying system, and hence, controller design procedure is not simple and some parameters like controllability indices are not constant in general, we still have some difficulties for designing linear controller for such systems. The author et.al. proposed the simple design procedure of pole placement controller for linear time-varying multi-input systems. The feedback gain can be obtained directly from the plant parameters without transforming the system into any standard form. This design method will be applied to the problem of stabilization of some desired trajectory of nonlinear systems.