Asynchronous Control for Discrete Semi-Markovian Switching Models Under Quantization

This study investigates the asynchronous stabilization for discrete semi-Markovian switching systems under input quantization. The jumps between different modes are based on the framework of incomplete semi-Markov kernel information, which is more general than the traditional Markovian process. Owing to an asynchronous phenomenon between the system mode and the control mode, a hidden semi-Markovian model is adopted to describe this mismatch situation. A logarithmic quantizer is used to characterize the quantized input signal before the data transmission. By using the Lyapunov function, a new stability condition is proposed for the underlying model. Finally, a space robot manipulator model is studied to verify the effectiveness of the designed controller.