Neither Zero nor Hold: Optimal Linear-Quadratic-Regulator State-Feedback Control Over Lossy Networks

This paper addresses the networked control design problem in which control packets are subject to dropout.We present an alternative to the two most straightforward compensation strategies available in the literature: the zero-input and hold-input strategies. The approach proposed in this note relies on transmitting extended control packets that carry additional information to be used whenever a control sample is lost. By means of convex optimization models, the problem is cast as a Linear-Quadratic-Regulator (LQR) optimal control formulation for a discrete-time Markov jump linear system, encompassing as particular cases the classical zero and hold strategies, as well as their generalized counterparts. Unlike existing approaches, the proposed formulation naturally extends to robust control of polytopic systems. Numerical experiments further compare the main techniques in the literature for this class of problems, highlighting the advantages of the proposed method.