Improved stability criteria for time-varying delayed T–S fuzzy systems via delay partitioning approach

This paper focuses on the stability analysis for uncertain Takagi–Sugeno (T–S) fuzzy systems with interval time-varying delay. The uncertainties of system parameter matrices are assumed to be time-varying and norm-bounded. Some new Lyapunov–Krasovskii functionals (LKFs) are constructed by nonuniformly dividing the whole delay interval into multiple segments and choosing different Lyapunov functionals to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the nominal and uncertain T–S fuzzy systems in a convex way. These stability criteria are derived that depend on both the upper and lower bounds of the time derivative of the delay. By employing the new delay partitioning approach, the obtained stability criteria are stated in terms of linear matrix inequality (LMI). They are equivalent or less conservative while involving less decision variables than the existing results. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results.

► These stability criteria depend on both the upper and lower bounds of the time derivative of the delay.
► Employ some new Lyapunov–Krasovskii functionals (LKFs) to further reduce the conservatism than some existing ones.
► Estimate a tighter upper bound of the derivative of the LKFs by an integral inequality.