Stabilization of fuzzy systems with input and state delays

In this study, a stabilization problem for continuous-time fuzzy systems subject to multiple time-varying delays in both state and input variables is addressed. Based on Lyapunov-Krasovskii functional and Pólya theorem, a sufficient stabilization condition is stated in terms of LMIs. Therefore, stabilizing controllers can be obtained easily with existing convex algorithms. Unlike existing methods, polynomial theory is used to deal with input-delay term u(t - σ(t)) since this delay term introduces an additional summation after defuzzification. Lastly, an example is given to illustrate the advantages of the proposed machinery, yielding more relaxed results when compared to existing methods.