Design of distributed sampled‐data fuzzy controller for a class of non‐linear hyperbolic PDE systems: input delay approach

Abstract

This study addresses the problem of distributed sampled-data fuzzy controller design for a class of non-linear distributed parameter systems which are described by first-order hyperbolic partial differential equations (PDEs). To achieve this goal, first, the non-linear system is modelled by a continuous-time Takagi–Sugeno first-order hyperbolic PDE fuzzy model. Subsequently, the authors design a new distributed sampled-data fuzzy controller that generates a zero-order hold sampled-data control signal appropriate for the PDE systems. Then, a new Lyapunov–Krasovskii functional is suggested to provide the stability analysis conditions of the closed-loop control system. Moreover, the stabilisation conditions are obtained and converted to linear matrix inequalities using some new null terms. The proposed technique has removed the structural constraints on the convection and Lyapunov matrices. Finally, the proposed approach is applied on a biological system and a non-isothermal plug flow reactor.