Quantized H∞ Feedback Control of Semi-Markov Jump Systems With Limited Mode Information

This paper concerns the quantized H_∞ feedback control problem for a class of semi-Markov jump systems with limited mode information. In networked control loop, the network-induced phenomenon limits the accuracy of the signal transmission. The mode of the jump system is thus hardly synchronized with the mode of the designed controller. To well address this asynchronous scenario, we introduce a hidden semi-Markov model to quantitatively describe its degree by setting a conditional probability, which further is assumed to be not completely known considering the sensor or measurement approach limitations. The control signal is to be quantized by a logarithmic quantizer before being transmitted to the actuator. Under the framework of Lyapunov theorem, sufficient conditions are presented by linear matrix inequality techniques to eliminated the quantization effects and ensure the stability of the closed loop system with a prescribed H_∞ performance. The parameterization scheme of the quantized feedback controller is finally given. A numerical example is presented in the end to illustrate the validity of the proposed results.