Quantized fuzzy passification for nonlinear systems with Markov-based transmission delays

In this paper, the quantized fuzzy passification issue for nonlinear systems subject to random transmission delays is studied. A discrete-time homogeneous Markov chain, whose state transition probability matrix is partially unknown, is employed to model the random transmission delays. And a logarithmic quantizer is introduced to overcome the channel capacity constraint. A sufficient condition is derived by constructing a Lyapunov function, which depends both on the fuzzy basis and the transmission delay, to guarantee that the augmented closed-loop system is mean-square exponentially stable and passive in the sense of expectation. Then, the controller is designed with the linearization of this condition. Finally, the effectiveness of the proposed design technique for nonlinear systems is demonstrated through a numerical example.