Spatiotemporal event-triggered anti-disturbance control for Markov jump LPV-PDE systems via disturbance observer

Abstract

This paper proposes a disturbance observer-based spatiotemporal event-triggered anti-disturbance control method for Markov jump linear parameter-varying partial differential equation (LPV-PDE) systems subject to disturbances. Based on the Takagi–Sugeno (T–S) fuzzy model, the original nonlinear system is approximated as a fuzzy LPV-PDE system. To reduce the number of sensors, pointwise measurements are introduced, based on which a spatiotemporal event-triggered mechanism is employed to alleviate the communication burden. Furthermore, a disturbance observer is developed to estimate the unknown disturbances modeled by an exogenous system. A fuzzy anti-disturbance point controller is then designed by combining the observer output with traditional state feedback. Sufficient conditions for the fuzzy LPV-PDE system to be exponentially stable are given by constructing a Lyapunov–Krasovskii functional (LKF). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed strategy.