Optimal tracking for linear systems with multiplicative noises

This paper studies optimal tracking control design for a single input single output (SISO) linear feedback discrete-time systems with multiplicative noises in control inputs. Such multiplicative noise can be used to characterize quantization errors or packet loss in a fading channel. Optimal mean-square control in tracking unit step reference signal is formulated and solved. It is shown that this optimal control design problem is an eigenvalue problem (EVP). The optimal design algorithm is developed.