Minimax Control of MIMO Systems over Multiple TCP-like Lossy Networks

This paper considers a minimax control problem over multiple packet dropping channels. The channel losses are assumed to be Bernoulli processes, and operate under the transmission control protocol (TCP); hence acknowledgments of control and measurement drops are available at each time. Under this setting, we obtain an output feedback minimax controller, which are implicitly dependent on rates of control and measurement losses. For the infinite-horizon case, we first characterize achievable H∞ disturbance attenuation levels, and then show that the underlying condition is a function of packet loss rates. We also address the converse part by showing that the condition of the minimum attainable loss rates for closed-loop system stability is a function of H∞ disturbance attenuation parameter. Hence, those conditions are coupled with each other. Finally, we show the limiting behavior of the minimax controller under the disturbance attenuation parameter.