Fault Estimation Design for Head-Two-Arms-Trunk System in T-S Fuzzy model

To provide insight into posture control strategies in patients with complete spinal cord injury (SCI), we estimate internal variables and unknown faults in patients with SCI using unknown input (UI) observer techniques. For the convenience of design and analysis, SCI patients are simulated with Head- Two-Arms- Trunk (H2AT) model, which belongs to a class of nonlinear description system. In order to design the unknown input observer, the model is expressed in a specific nonlinear Takagi-Sugeno (TS) fuzzy form, which allows all unmeasurable premise variables to be separated in the nonlinear afterparts. Using Lyapunov stability theorem, sufficient conditions to design the unknown input observer are derived in the form of linear matrix inequalities, conveniently solved by convex optimization techniques. Simulation results demonstrate the effectiveness of the proposed observer design.