Quantized Output Feedback Tracking Control for Discrete-Time Periodic Markov Jump Systems With Packet Loss Compensation

The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> static output feedback tracking control issue for discrete-time periodic Markov jump systems with quantization and packet loss is explored. The packet loss follows Bernoulli random distribution, which assumes that the packet is discarded in a probabilistic manner before being transmitted to the controller. On this basis, considering the restricted network bandwidth, a novel quantization-based packet loss compensation scheme using single exponential smoothing approach is firstly given to help offset the influence of network congestion and missing packets. Then, an output feedback tracking controller is firstly designed to minimize the tracking error between the system output and the given reference model output. Aiming at the loss of mode information, the tracking controller designed is partially mode-dependent. Furthermore, by giving a mode-dependent Lyapunov function with periodicity, the sufficient condition for the existence of this controller is derived to ensure the stability of the tracking error system with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance. Ultimately, the effectiveness and practicality of the developed technique are demonstrated through an example of a single-link robotic arm model. Note to Practitioners—In real life, periodic systems generated by random mutations can be seen everywhere, such as economic systems. This type of system undergoes structural or parameter changes within a single operating period due to sudden changes in the external environment. Periodic Markov jump systems (PMJSs) can effectively describe complex systems with both periodic and stochastic characteristics. To address the adverse effects of quantization and packet loss, a new packet loss compensation strategy based on single exponential smoothing method and quantization is proposed. On the other hand, research on output feedback tracking control is crucial for fields such as missiles and spacecraft. To ensure that the system can operate according to the specified trajectory, a new design method for a periodic output feedback tracking controller has been proposed. And this type of controller effectively solves the tracking problem of PMJSs with quantization and packet loss.