Observer-based Control of Two-Time-scale Markov Networked Control Systems Based on Coding-Decoding Scheme

This paper addresses the observer-based control problem for two-time-scale Markov networked control systems operating under a coding-decoding scheme. To overcome communication bandwidth limitations and safeguard data privacy, the discrepancy between the observer state data and the designed duplicator decoded data is encoded into a specific sequence of codewords before transmission. The decoder converts these codewords into decoded forms upon receipt. A theoretical framework for the coding-decoding scheme is established using a uniform quantization method to derive criteria ensuring system detectability. Based on this framework, a decoded state-dependent controller is designed, and sufficient conditions for the stability of the estimated error system are provided. By constructing appropriate Lyapunov functions and utilizing the linear matrix inequality method, a sufficient condition for the exponential mean-square boundedness of the closed-loop system is derived. Numerical simulation demonstrates the effectiveness of the proposed control scheme.