The existing models for studying sitting stability are not valid to estimate internal forces and torques for people living with a complete spinal cord injury who will use their upper limbs instead of their lower back and abdominal muscle. The aim of this work is to design an unknown input observer (UIO) based on a so-called H2AT nonlinear model. To cope with the high nonlinearity of the model, the Takagi-Sugeno (TS) formalism is used and the observer convergence is proved via linear matrix inequalities (LMI) constraints solving. A control is also derived in simulation in order to stabilize the nonlinear model and to assess the observer ability to estimate unknown inputs. Then motion data of four subjects living with complete SCI are used to compare the internal forces developed and analyze stabilization strategies. Combining a nonlinear model with a fuzzy T-S descriptor, UIO represents a new and successful approach to characterize sitting postural control.