Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence Method

Abstract

A satellite is considered to be moving relative to a nominal elliptical orbit, whose dynamics are usually described by the Tschaunner-Hempel equation (T-H equation). In this paper, we propose to transform the second-order time-varying system represented by the linear T-H equation with a second-order matrix form into a first-order time-varying system. Then, the controllability of the first-order time-varying system is investigated with the matrix sequence method including $e=0$ . Meanwhile, we study the observability of the first-order time-varying system with a specific form of measurement. The advantages of the matrix sequence method for controllability and observability analysis are tested by numerical examples, respectively. Dual theory is used to investigate the controllability and observability of the corresponding dual system of the T-H equation. The corresponding conclusions are obtained.