Sampled-Data Control for IT-2 Fuzzy Systems With Packet Losses: Fragmentation-Based Integral Inequality Technique

The focus of this work is on establishing stabilization criteria for interval type-2 (IT-2) fuzzy systems with packet losses using a memory-based sampled-data controller (MBSDC) approach. To accomplish this, first, a new fragmentation-based integral inequality (FBII) is proposed with a more accurate estimation. Additionally, considering a fractional coefficient within the range of
$0 < \delta < 1$
, the sampling intervals are divided into four distinct nonuniform segments. These segments encompass the complete sampling details of the intervals:
$[\xi _{\iota }, \xi _{\iota } + \delta \nu _{1}(\xi))$
,
$[\xi _{\iota } + \delta \nu _{1}(\xi), \xi)$
,
$[\xi, \xi + \delta \nu _{1}(\xi))$
, and
$[\xi + \delta \nu _{1}(\xi), \xi _{\iota +1})$
. Simultaneously, a novel and improved looped-functional is formulated, incorporating both sampling information and transmission delay details. Subsequently, employing the devised FBII technique, specific sufficient conditions are established using linear matrix inequalities (LMIs) to ensure asymptotic stability of the augmented closed-loop systems with respect to the
$H_{\infty }$
-performance index
$\psi $
in the presence of packet losses. Finally, numerical simulations of the Takagi–Sugeno (T–S) fuzzy-based PMSM and mass–spring model are presented, showcasing the effectiveness and superiority of the suggested methodology.