## 1 Introduction
Consequently, the possibility of adverse effects on the robustness of the attitude control system cannot be excluded. Moreover, it is mathematically difficult to find a correct solution because the solution by the pseudo inverse method is the maximum likelihood solution, and the condition number of the matrix becomes extremely large near singularity (Jacobian matrix is ill-conditioned). Thus, an accurate solution cannot be calculated in some cases when the Jacobian matrix is ill-conditioned because calculation errors owing to round-off errors are greatly amplified [14; 15]. As a countermeasure, regularization methods of the matrix for reducing calculation errors have been proposed, but the calculation costs tend to be high because repetitive calculation is necessary [14; 15; 16]. Considering actual operation, rounding errors are likely to be included because of the restrictions on the performance of the on-board computer. In addition, since the Jacobian matrix is time-varying, it is necessary to solve the regularization method in every control cycle. Therefore, it is considered that it is difficult to calculate an accurate solution of the pseudo inverse method in the on-board computer under a singularity where the calculation errors become large. Consequently, it is considered that a control system for calculating the control input to the SGCMGs is necessary without solving the pseudo inverse matrix. In view of the above background, an attitude control system that can generate the gimbal angular velocity input without solving inverse kinematics (as the main control system), is required, as shown in lower part of Figure 2. Accordingly, we will integrate the satellite and SGCMGs and design a model with the gimbal angular velocity as the control input. To realize this, state-dependent linear representation (SDLR) in the state-dependent Riccati equation (SDRE) controller [17; 18] is used. This proposed control system is able to gain attitude stability and robustness even in a singularity because the optimal gimbal angular velocity input is guaranteed by the SDRE controller. Furthermore, by designing SDLR with an error representation, it is possible to guide to the gimbal angle, which is advantageous for the next attitude maneuver. Additionally, singularity avoidance/escape steering is explicitly considered by taking into account the relation between the biased state-dependent weighting (BSDW) matrix for the gimbal angular velocity input and the SGCMG steering with respect to the maneuver axis. This steering of gimbals is realized by adding to each SGCMG with bias. In the numerical analysis, we verify the effectiveness of the agile large-angle attitude maneuver by the proposed control system consisting of an SGCMG-integrated satellite model (SISM) and BSDW. In addition, the analysis shows that the convergence to the target satellite attitude is guaranteed by the optimality of the gimbal angular velocity input. Furthermore, we verify the robustness against the moment of inertia which is likely to contain an error in model identification on the ground. However, a general robustness analysis of SDRE has not been determined. Therefore, as an initial study, the true values used for updating the state quantity of the plant are set in several patterns with respect to the identification values.