Optimal tracking performance of discrete-time systems with quantization

This paper studies optimal tracking performance issues for linear time invariant system with two-channel constraints. The specific problem under consideration is quantization for up-link and down-link communication channel which satisfies some constraints. Logarithmic quantization law is employed in the quantizers. The tracking performance is defined in an square sense, and the reference signal under consideration in this paper is a step signal. The system’s reference signal is considered as a step signal. The tracking performance is measured by the minimum mean square error between the reference input and the system’s output. By using dynamic programming approach, discrete-time algebraic Riccati equation (ARE) is obtained. The optimal tracking performance is obtained by output feedback control, in terms of the space equation of the given system and the unique solution of the discrete-time algebraic Riccati equation. And, the impact of quantizer for optimal tracking performance is analyzed. Finally, simulation example is given to illustrate the theoretical results.