Quantized Output Feedback Tracking Control for Discrete‐Time Markov Switching Repeated Scalar Nonlinear Systems via Dual Periodic Hidden Markov Models

ABSTRACT

This paper investigates the quantized output feedback tracking control problem for discrete‐time periodic Markov switching repeated scalar nonlinear systems. To reduce the communication burden, a mode‐dependent logarithmic quantizer is employed to quantize the transmitted output signal, and a mode‐dependent periodic output feedback tracking controller is constructed. Since, the quantizer, the controller, and the plant operate asynchronously, a dual periodic hidden Markov model framework is proposed to describe the asynchronous phenomena, where both the transition probability matrices and the conditional probability matrices are allowed to be partially unknown. By constructing a mode‐dependent periodic Lyapunov function, sufficient conditions are derived to guarantee the stochastic stability and performance of the tracking error system. Finally, the feasibility of the proposed method is verified through a cognitive radio network model.