Joint State and Parameter Estimation for Discrete-Time Takagi-Sugeno Model

Takagi-Sugeno (T-S) models have been popular in analyzing nonlinear systems. Observer designs for T-S models have focused on both cases with measured and unmeasured premise variables. However, the unmeasured premise variables have to be one of the states of the system. If one of the inputs is a premise variable, these approaches are not applicable. A recent literature proposed a joint state and parameter estimation for time-varying unknown parameters in systems of a special type [1]. A discrete-time version of the results is developed in this paper. The modeling approach is described and the stability analysis of the estimation is given using the Lyapunov method with the L-2 approach handling the uncertainties.