Design of Observers for Takagi-Sugeno Systems with Immeasurable Premise Variables: an ℒ2 Approach

A new observer design method is proposed for Takagi-Sugeno systems with immeasurable premise variables. Since the state estimation error can be written as a perturbed system, then the proposed method is based on the L2 techniques to minimize the effect of the perturbations on the state estimation error. The convergence conditions of the observer are established by using the second method of Lyapunov and a quadratic function. These conditions are expressed in terms of Linear Matrix Inequalities (LMI). Finally, the performances of the proposed observer are improved by eigenvalues clustering in LMI region.

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