State Estimation for Nonlinear System Using Line Integral Lyapunov Function: A Polytopic Approach With Unmeasurable Premises

This paper describes an approach for design a new observer based on the mean value theorem and analyzing the stability of a continuous-time Takagi-Sugeno fuzzy system with unmeasurable premise variables through the line-integral Lyapunov function approach. The stability conditions are more general and relaxed than those obtained through conventional quadratic Lyapunov functions, which can be expressed as linear matrix inequality forms, these contraints can be solved using linear programming approch via specialized software tools. A implementation on Flexible joint robot was performed, resulting in findings that clearly demonstrate the effectiveness and efficiency of the proposed method.