Stabilization of positive Takagi-Sugeno fuzzy discrete-time systems with multiple delays and bounded controls

This paper deals with the problem of stabilization by state feedback control of Takagi-Sugeno (T-S) fuzzy discrete-time systems with multiple fixed delays while imposing positivity in closed-loop. The obtained results are presented under linear programming (LP) form. In particular, the synthesis of state feedback controllers is first solved in terms of Linear programming for the unbounded controls case. This result is then extended to the stabilization problem by nonnegative controls, and stabilization by bounded controls. The stabilization conditions are derived using the single Lyapunov-Krasovskii functional (LKF). An example of a real plant is studied to show the advantages of the design procedure. A comparison between linear programming and LMI approaches is presented.