Stabilizing bit rate conditions of linear systems under DoS attacks without acknowledgments

Abstract

This paper is concerned with the quantized stabilization of linear systems under denial-of-service (DoS) attacks. In particular, we investigate the systems without acknowledgment (ACK) signals from the decoder to the encoder. Moreover, the concerned systems are also subject to transmission delay and bounded process noise. The major challenge of the quantized control strategy design lies in the absence of ACKs, which may break the synchronization between the encoder and decoder. This challenge is addressed by a novel control strategy under which redundant symbols are encoded and transmitted after sampling. Large transmission delay can be tackled by our strategy as long as more bit rates are used. To further save communication bandwidth, event-triggered sampling is applied. We derive sufficient bit rate conditions for the input-to-state stability (ISS) of the system, which depends on the unstable eigenvalues of the system, the transmission delay, and the DoS parameters. Moreover, we give the DoS conditions under which the derived stabilizing bit rate conditions can be lower than the minimum bit rate condition for systems under periodic sampling with ACKs. A numerical example is given to verify our results.