The 'Peak' Effect in Guidance Stabilization

摘要

A controllable linear control system is considered. According to the Pole assignment theorem, there exists an appropriate linear feedback which generate a linear differential equation with any given set of eigenvalues. It is shown that there is a large deviation of the solutions from the equilibrium position at the beginning of the stabilization process, that is, trajectories have "peaks" before damping to the equilibrium point when the module of the eigenvalues is very small or very big. This effect is of interest for guidance stabilization of nonlinear systems.