H∞ - Optimal Control over erasure channel

In this paper, the optimal H∞ control of a linear time invariant (LTI) networked control system (NCS) over a lossy network is analyzed. Specifically we consider a TCP-like data network where packet drops are modelled using a two-state Markov process. By employing the theory of dynamic games, a state-feedback H∞ controller is obtained. It is shown that, subjected to a suitable H∞ disturbance attenuation level and suitable packet loss probabilities, such a controller exists for both finite and infinite horizon cases. We also show the asymptotic stability of the NCS in the mean-square sense. Finally a numerical example is presented to demonstrate our work.