H∞ control for discrete-time nonlinear Markov jump systems with multiplicative noise and sector constraint

This paper addresses the finite horizon H∞ control problem for a class of discrete-time nonlinear Markov jump systems with multiplicative noise and nonlinear feedback device. The system nonlinearity occurs in a random way specified by a Bernoulli process, whereas the actuator and sensor nonlinearities are restricted to a sector region. Both the state and the dynamic output feedback H∞ controllers are devised in terms of difference LMIs. The proposed approach not only allows the resulting system to achieve a prescribed disturbance attenuation level, but also enables the output of actuator/sensor to meet the designated sector condition. Moreover, it is also shown that our approach is well-Adapted for dealing with the discrete-time Markov jump systems with saturated actuator and sensor. Finally, a backward iterative algorithm is provided to solve the obtained difference LMIs and a numerical example is presented to verify the efficiency of the theoretical results.