Design and stability analysis of an aircraft pitch axis control system has been a well studied problem, [1], [2]. Some researchers, [1], determined analytically the stability regions of a F-14 in terms of the engine thrust and pitch attitude and presented a global stability result for nonlinear modeled pitch axis of a F-14 modulated by a nonlinear dynamic inversion control law. Recently, a new computationally tractable nonlinear system analysis method was proposed, [3]. From a computation perspective, the method relaxes searching for positive semi definite stability certificate functions (eg. Lyapunov functions) to searching for sum of squares (of appropriate polynomials) certificate functions. Solving for the relaxed requirement leads to solving a SDP (Semi Definite Program) which is computationally tractable. This approach was used for Lyapunov function synthesis, [4] and estimating the stability region of SDRE (State Dependant Riccati Equation) systems, [5]. A recently developed software, SOSTOOLS (v1.01), [6] was used to convert the required sum of squares conditions to an appropriate SDP which was then solved using SeDuMi, [7]. In this paper we determine, numerically, the region of attraction of a trim point for the pitch axis of a nonlinear modeled aircraft modulated via a linear dynamic inversion based controller. The model incorporates uncertainty in the position of center of gravity along X-body axis. The stability regions are computed using SOSTOOLS.
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