Observer-Based Control of Networked Periodic Piecewise Systems With Encoding–Decoding Mechanism

This article deals with the observer-based control problem of networked periodic piecewise systems under encoding-decoding frameworks. An encoder with a uniform quantizer, which can compress and encrypt data, is provided to process the measurements from the sensors. The processed data is transmitted over the network to the decoder to recover the original data and then to the remote control station, thereby reducing the communication burden and ensuring data security. Then, by constructing the periodic Lyapunov function with linear interpolation terms, exploiting an effective technique—singular value decomposition—sufficient conditions with linear matrix inequality (LMI) constraints for selecting the observer and controller parameters are derived to achieve the exponentially ultimate boundedness of closed-loop systems. Moreover, to eliminate extra steady-state errors caused by encoding-decoding mechanisms (EDMs), a dynamic quantization factor that can make the asymptotic upper bound tend to zero is designed. Finally, numerical examples are provided to illustrate the effectiveness of the derived theoretical results.