Stability Domain Estimation for Dynamic Inversion Embedded SDRE Flight Controller

The Dynamic Inversion embedded SDRE control law combines dynamic inversion and state dependent riccati equation techniques such that the desired dynamics required for dynamic inversion is calculated by solving an SDRE. The resulting closed loop system is similar to a pure SDRE controller. This controller has been previously applied to the control of the rotational dynamics of a flight vehicle and simulations have shown that the origin of the closed loop system is a locally asymptotically stable equilibrium point. The stability of SDRE controlled systems have been previously studied in literature, however, it is still dicult to show global stability properties for this controller. The analytical solution of the state dependent riccati equation is possible for systems of order less than or equal to 2 by choosing the state dependent system matrix carefully. The global stability properties can then be determined by studying the analytical expression of the closed loop system. The stability of SDRE controlled systems of order greater than 2 such as the rotational dynamics of a flight vehicle are determined by calculating the Domain or Region Of Attraction (ROA) around the equilibrium point. A method for estimating the ROA of a nonlinear system by defining an overvaluing matrix using vector norms has been extended in past literature to calculate the stability domains for SDRE controlled systems. In this paper, we use this method of vector norms to analyze the stability properties of the DISDRE controlled rotational dynamics of a flight vehicle and illustrate our results with a Region of Attraction around the origin of the closed loop system.