Sampled-Data Fuzzy Control for Nonlinear Delayed Distributed Parameter Systems

Abstract

Under spatially local averaged measurements (SLAMs), this article introduces a sampled-data fuzzy control (SDFC) for nonlinear delayed distributed parameter systems (DDPSs). First, we use a Takagi–Sugeno (T–S) fuzzy parabolic partial differential-difference equation (PDDE) to accurately describe the nonlinear DDPS. Then, on basis of the T–S fuzzy PDDE model, an SDFC design under SLAMs via space-dependent linear matrix inequalities (SDLMIs) is subsequently developed to ensure the exponential stability of the closed-loop nonlinear DDPSs by using inequality techniques and Lyapunov functional, where slow-varying and fast-varying delays are respected. Furthermore, to solve SDLMIs, the SDFC design problem for nonlinear DDPS under SLAMs is formulated as a linear matrix inequality feasibility problem. Finally, numerical simulations of two examples are presented to support the given SDFC strategy.