Mixed H∞ and passivity-based resilient controller for nonhomogeneous Markov jump systems

In this paper, the robust mixed H∞ and passivity-based control problem is investigated for a class of discrete-time Markov jump nonlinear systems with uncertainties, quantization and time-varying transition probabilities. In addition, the time-varying transition probability matrices in the considered system are described by a polytope set. Further, the measurement size reduction technique is implemented which consists of two factors, namely, the logarithmic quantization and the measurement element selection scheme. In order to reflect the imprecision in controller implementation, the additive controller gain problem is considered. Based on the Lyapunov stability theory, a new set of conditions is derived such that the resulting closed-loop Markov jump system is stochastically stable with a prescribed mixed H∞ and passivity performance index. Finally, the effectiveness of the proposed control scheme is illustrated by two numerical examples including an application example based on a DC motor device.