Guaranteed cost sliding mode control of Markovian jump Lur'e systems under Round-Robin protocol

This study copes with the guaranteed cost problem for a class of Markovian jump Lur'e systems via sliding mode control technique, in which the scheduling of controller signals towards the actuators is regulated by the Round-Robin protocol. This means that at each transmission instant, only one actuator node can access the transmission network and the other actuators cannot obtain any new control information. In order to deal with this phenomenon, an updating rule as compensator is proposed, based on which the other actuators utilise the past control signals stored in the corresponding buffers. Then, a mode-token-dependent sliding mode controller is designed, in which the characteristic of the Lur'e non-linearities is involved. Furthermore, by introducing a new token-dependent Lur'e-type Lyapunov function, the stochastic stability of the resultant closed-loop systems is analysed, and the guaranteed cost performance is attained. Finally, a dynamic Leontief input-output model is adopted to illustrate the proposed method.