Satellite Formation Flying Control Design using Transformation Allergic Indices in the Relative Motion Dynamics Matrix

In this paper (with its IP protected contents), we introduce a new approach or philosophy (different from the one used in the current literature) which is labelled as Transformation Allergic (TA) approach or philosophy, for analyzing the stability (real state variable convergence) issue of any real Linear Time Invariant State Space (LTISS) system. The current literature’s Hurwitz stability concept is shown to be insufficient for guaranteeing the convergence of all real state variables obtained by various real linear combinations arising due to the use of arbitrary, linear, non-singular transformations (orthogonal as well as non-orthogonal) on the original given real state variables. In this paper, we focus on the problem of controlling satellite formation flying using the Clohessy-Wiltshire Relative equations of motion as the motivational application for demonstrating the usefulness of the proposed TA approach of this paper. To contrast the proposed TA approach conditions with the current literature conditions, we label the current literature conditions as Transformation Compliant (TC) conditions. This paper’s findings suggest that the satellite formation flying dynamics with a controller designed by the proposed TA conditions of this paper, provide not only enhanced stability robustness but also offer reduced fragility for the controller in its implementation. The proposed control design, based on sign pattern analysis, offers other advantages such as reduced control effort and improved robustness to real life parameter perturbations which are lacking in the current literature control design methods such as Pole Placement design and LQR design.