Fuzzy Observer Stabilization for Discrete-Time Takagi-Sugeno Uncertain Systems with k-Samples Variations

In this paper, we analyze the problem of the stabilization for discrete-time Takagi-Sugeno fuzzy parametric uncertain systems. The stabilization conditions of these systems are investigated with two observers and two different Lyapunov functions: nonquadratic and delayed nonquadratic. The stabilization conditions are analyzed between k and k + t sample variations in the Lyapunov function. The obtained stabilization results represent an extension of previous works with one-sample variation in discrete time. All the results are obtained in the form of linear matrix inequalities which are solved by using various convex optimization algorithms. Two theorems are proposed, and comparison via simulation is given to demonstrate the robustness of the proposed approaches. Nevertheless, this paper shows that the second proposed observer gives the less conservative results (less restrictive). These reduced conservative results are demonstrated by a larger feasible area of stabilization (stabilization domain) and a fast convergence of estimation errors compared to the first.