Linear Time-Periodic System
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
A linear system whose coefficient matrices vary periodically with time, satisfying A(t+T)=A(t), B(t+T)=B(t). It is the simplest and most important class of time-varying systems; many aerospace time-varying systems can be approximated as LTP (e.g., dynamics on elliptic orbits, attitude motion of spinning rigid bodies). The error dynamics of Halo orbit tracking, after first-order linearization, naturally has this structure: the state matrix A(t) obtained by linearizing the CR3BP equations along the nominal orbit is a periodic function.
Application Value
Linear time-periodic system theory applies to elliptical orbit dynamics and periodic orbit tracking control, forming the theoretical basis for Halo orbit maintenance strategies.
Related Concepts
- Variable Structure Sliding Mode Control
- Pontryagin Minimum Principle
- Error Function
References
- 徐明和徐世杰 - 2008 - Halo轨道维持的线性周期控制策略