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 c-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 e-dependent stabilization conditions as a set of e-independent linear matrix inequalities that are easily solved. On this basis, the upper bound of singular perturbation parameter e, i.e., e(*), should be determined to compute the fast MASTI for the possibly slow sampling of fast states. The optimal match of (e(*), 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.

Automated summary

This article discusses the design of a control synthesis method for singularly perturbed nonlinear systems under a nonperiodic multirate sampling mechanism, and provides guidance on the choice of maximum allowable sampling time intervals for multirate sensors. The sampled system is converted into a fuzzy singularly perturbed model, and sufficient conditions for stabilizing the multirate sampled system are derived. A linear matrix inequality-based design method is proposed, and the upper bound of the perturbation parameter is determined to compute the maximum allowable sampling time interval for fast states. The optimal match is detected for a tradeoff among stability, performance, and cost. The obtained results are demonstrated in an example system.