Nonperiodic Multirate Sampled-Data Fuzzy Control of Singularly Perturbed Nonlinear Systems

Choosing adequate sampling frequencies in sensors has a considerably positive impact on the two time scale fuzzy logic controller design. Motivated by this concept, this article addresses the fuzzy-parallel distribution compensation (PDC)-based control synthesis for a singularly perturbed nonlinear systems (SPNS) under a nonperiodic multirate sampling mechanism, which also provides guidance on the reasonable choice of maximum allowable sampling time intervals (MASTIs) for multirate sensors. First, the sampled SPNS is converted into a continuous-time Takagi-Sugeno fuzzy singularly perturbed model (TSFSPM) with slow and fast time-varying delays. Then, an $\epsilon$-dependent Lyapunov-Krasovskii functional of order $n$ is proposed to derive the sufficient conditions for stabilizing a multirate sampled TSFSPM under a two time scale PDC control. Given the slow MASTI, an efficient linear-matrix-inequality-based design is proposed to recast the $\epsilon$-dependent stabilization conditions as a set of $\epsilon$-independent linear matrix inequalities that are easily solved. On this basis, the upper bound of singular perturbation parameter $\epsilon$, i.e., $\epsilon ^*$, should be determined to compute the fast MASTI for the possibly slow sampling of fast states. The optimal match of $(\epsilon ^*,n)$ is detected for a tradeoff among the closed-loop stability, the controller performance, and the sensor cost. The superiority of the obtained results is shown in an example of a flexible joint inverted pendulum system.