Optimal control of linear discrete-time systems with quantization effects

This paper studies optimal control designs for networked linear discrete-time systems with quantization effects and/or fading channel. The quantization errors and/or fading channels are modeled as multiplicative noises. The H₂ optimal control in mean-square sense is formulated. The necessary and sufficient condition to the existence of the mean-square stabilizing solution to a modified algebraic Riccati equation (MARE) is presented. The optimal H₂ control via state feedback for the systems is designed by using the solution to the MARE. It is a nature extension for the result in standard optimal discrete-time H₂ state feedback design. It is shown that this optimal state feedback design problem is eigenvalue problem (EVP) and the optimal design algorithm is developed.