Control of Jump Linear Systems Over Jump Communication Channels - Source-Channel Matching Approach

The control of partially observed jump linear systems over jump communication channels is investigated when the Plant State Information (PSI) and the Channel State Information (CSI) are present at the transmitter and the receiver side of the communication channel. The PSI refers to the state of a Markov chain driving the plant dynamics, while the CSI is the state of a Markov chain driving the communication channel. Necessary conditions for observability and stabilizability in probability and r-th mean are derived by using information transmission theorem and Shannon´s lower bound on the rate distortion. Based on the source-channel matching principle, a transmission technique is designed that achieves observability and stabilizability of the controlled jump system in mean-square sense.