This paper introduces a modelling approach to investigate seated postural stability for subject suffering a complete spine cord injury (SCI). A mechanical model, variation of the double inverted pendulum, is used to represent a subject in the sagittal plane moving back and forth his uppers limbs and head to maintain his stability. A non-linear descriptor system is obtained by developing the Lagrangian equations and then written as a Takagi-Sugeno model. An Unknown Input Observer (UIO) is then used to estimate the system state and the unmeasured internal stabilizing force. Simulations results attest that this technique can be used to non invasivaly recreate unmeasured data and contribute to a better understanding of how people with complete spine cord injury maintain their stability.