Bit-Rate Conditions to Stabilize a Continuous-Time Linear System With Feedback Dropouts

This technical note considers the input-to-state stability of a continuous-time linear system, which sends feedback signals from the sensor to the controller over a nondeterministic communication network with bounded network delay and occasional dropouts. Not only the bits inside each feedback packet, but also the sampling time instant of that packet can carry information. Due to processing delay and network delay, the controller cannot precisely know the sampling time of a packet and can only approximate it with the receive time instant of that packet. The difference between the sampling and receive time instants of a packet is referred to as timing error, which reduces the amount of information extracted from the receive time instant. By additionally extracting information from receive time instants of feedback packets, we may stabilize the concerned system in the input-to-state sense at a lower bit rate than the approaches utilizing only the bits inside feedback packets. Besides timing error, nondeterministic dropouts of feedback packets may also harm the stability of the concerned system. By simultaneously considering timing error and feedback dropouts, we derive some stabilizing bit-rate conditions that are determined by the unstable eigenvalues of the system matrix, the dropout rate, and the upper bound on the timing error. These stabilizing bit-rate conditions are not disturbed by bounded process noise.