Regular Perturbation Analysis for Trajectory Linearization Control

Trajectory linearization control (TLC) is a nonlinear control design method, which combines an open-loop nonlinear dynamic inversion and a linear time-varying feedback stabilization. TLC achieves exponential stability along the nominal trajectory, therefore it provides robust stability and performance. In this paper, stability analysis of TLC with regular perturbation is presented. By integrating the Lyapunov second method with the linear time-varying (LTV) system spectra theory, which is a first method of Lyapunov. The analysis assesses stability robustness of TLC and identifies its relationship with the closed-loop PD-eigenvalues. Thus the analysis provides a guideline to design and real-time tuning of the time-varying closed-loop PD-eigenvalues.