Networked Stabilization with Multi-periodic Sampling and Packet Dropout

This paper presents a co-design method for the networked mean square (MS) stabilization problem of multi-input systems with multi-periodic sampling over packet dropout channels, where the control law is sampled with different sampling period and then transmitted via communication channels subject to data loss constraints. In order to solve this problem, a pair of encoder and decoder is introduced for fully utilizing the resource of communication channels. A solvability condition is conducted and reveals the fundamental limitation among the H
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norm of the system, packet loss rates, and coding matrices. Finally, a numerical example is included to show the effectiveness of the current results.