Network-Based Quantized Control for Fuzzy Singularly Perturbed Semi-Markov Jump Systems and its Application

This paper deals with the quantized control problem for nonlinear semi-Markov jump systems subject to singular perturbation under a network-based framework. The nonlinearity of the system is well solved by applying Takagi–Sugeno (T-S) fuzzy theory. The semi-Markov jump process with the memory matrix of transition probability is introduced, for which the obtained results are more reasonable and less limiting. In addition, the packet dropouts governed by a Bernoulli variable and the signal quantization associated with a logarithmic quantizer are deeply studied. The major goal is to devise a fuzzy controller, which not only assures the mean-square $\bar { \sigma }$ -error stability of the corresponding system but also allows a higher upper bound of the singularly perturbed parameter. Sufficient conditions are developed to make sure that the applicable controller could be found. The further examination to demonstrate the feasibility of the presented method is given by designing a controller of a series DC motor model.