Tracking performance limitation of a linear MISO unstable system with quantized control signals

This paper studies the tracking performance for linear time-invariant multi-input single-output (MISO) discrete-time feedback systems with quantized control signals. The specific problem under consideration is that the quantized control signals transmitted to a given plant by two different communication channels which satisfy some constraint. The tracking performance is measured by the energy of the error response between the output of the plant and the reference signal. Logarithmic quantization law is used in the quantizers. To obtain the best attainable tracking performance of the feedback system, two parameter controller is adopted. By using stochastic dynamic programming approach, the best attainable tracking performance is in terms of the state equation of the plant and the largest relative quantization errors of the logarithmic quantization laws. Furthermore, a sufficient condition for asymptotical tracking is given for the feedback system in an average sense.