On the compensation of LQG over a lossy network utilizing previous control signals

In this paper we study the compensation problem of discrete-time LQG over a lossy network under TCP-like protocols utilizing previous control signal in the presence of control signal loss. We first show that two technical difficulties, one delay related and the other state inconsistency related, will be encountered when one attempts to analyze the effect from hold-input on the system as control loss occurs. Using a special technique presented in the paper that exploits the internal structure of the optimal feedback gain thus circumvents the above two difficulties, we show why direct use of hold-input may turn out to be inappropriate from closed loop stability standpoint. Following that we then show how it should be modified thus improving existing hold-input method and how the resulting compensation problem can be transformed into three kinds of static output feedback related problems that are easier to solve. A solution algorithm of the new reformulated problems is presented. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.