# Modeling and Control of Satellite Formations: A Survey
## 4 Leader-Follower Formation Architecture
This, along with the result of formulating the extended linear matrix inequality (LMI) for continuous-time systems, allows one to obtain explicit expressions for calculating the parameters of distributed controllers for both state feedback and dynamic output feedback. The main contribution of [135] is the solution of the distributed control problem for systems with continuous time under the conditions of \(H_{\infty}/\alpha\)-stability and \(H_{2}/\alpha\)-stability characteristics by solving the set of LMIs with non-common Lyapunov variables. The efficiency of this method is demonstrated by the example of a satellite formation. Autonomous navigation of micro-UAVs is usually based on the integration of inexpensive Global Navigation Satellite System (GNSS) receivers and inertial and magnetic sensors based on microelectromechanical systems (MEMS) for motion stabilization and control. The resulting navigation performance in terms of position and orientation accuracy may be insufficient for other mission tasks, such as those related to precise sensor pointing. In this context, [136] introduces a collaborative UAV navigation algorithm that allows the main vehicle equipped with inertial and magnetic sensors, a global positioning system (GPS) receiver, and a vision system to improve its navigation performance (in real time or in real-time). The focus is on the outdoor environment, and the key concept is to use differential GPS (DGPS) among vehicles and vision-based tracking (DGPS/Vision) to create a virtual auxiliary navigation sensor, which information is then integrated into a sensor fusion algorithm based on an extended Kalman filter (EKF). The developed concept and processing architecture are described with an emphasis on the DGPS/Vision orientation determination algorithm. Efficiency assessment is carried out on the basis of numerical modeling and flight tests. In the latter of these, the navigation estimates obtained from the DGPS/Vision approach are compared with the estimates provided by the onboard autopilot system of the tuned quad. The analysis shows the potential of the developed approach, mainly due to the ability to use magnetic and inertial-independent accurate orientation information. The distributed robust control method is developed relies, on a spaceborne distributed telescope, is presented in [137], where a combination of robust \(H_{\infty}\) control and distributed control using the consensus approach is proposed, focused on the application to satellite formation motion. The method of simultaneous control of the relative motion and orientation of the solar radiation pressure was proposed in [138]. The aim of the control is to stabilize a given closed relative orbit. The basic idea is to use special materials for solar sails that can change their optical properties. A solar sail consists of several rectangular cells. Each of them can change its optical properties. The required steering force is generated by varying the average reflectivity of the solar sail, and the steering torque is achieved using the appropriate black and white mesh pattern. [PERSON] et al. [139] discussed the use of sunlight pressure to control a satellite formation. The control is based on the rotation of the sail normal, which provides for a change in the optical properties of its surface. [PERSON] et al. [140] dealt with the problem of satellite formation immediately after launch. When detached from the launcher, there is a certain error in the magnitude of the speed jump, which leads to slightly different periods of rotation of the satellites. As a result,relative paths become open. Differential control using a resistance force is considered. The satellite orientation is controlled by a magnetic actuator. The problem of creating a robust formation controller for a group of satellites whose dynamics are associated with nonlinearities and uncertainties is considered by [PERSON] et al. [141].