Sampled‐data fuzzy control for non‐linear parabolic distributed parameter systems with control inputs missing

Abstract

In this study, an H ∞ sampled-data fuzzy control problem is considered for non-linear parabolic partial differential equation (PPDE) systems with control inputs missing. It is assumed that the actuator to the plant is set to zero if the control inputs missing which occurs in a random way satisfies a Bernoulli distribution. With the aid of the modal decomposition technique, a non-linear ordinary differential equation (ODE) system is initially obtained to represent the dominant dynamics of the PPDE system. Subsequently, a Takagi–Sugeno fuzzy model is utilised to accurately describe the resulting non-linear ODE system. Then, using a novel time-dependent functional and the stochastic analysis technique, an H ∞ sampled-data fuzzy controller with the stochastic missing data via linear matrix inequalities is proposed to stabilise exponentially the non-linear PPDE system in the mean square sense and achieve an H ∞ performance for the derived non-linear ODE system. Finally, an example on a temperature cooling fin is given to verify the proposed design strategy.