Quantized feedback control for 2D uncertain nonlinear systems with time-varying delays in a networked environment

In this paper, a feedback control problem is studied for a class of network-based two-dimensional (2D) uncertain nonlinear systems with time-varying delays described by the Fornasini-Marchesini (FM) second model. The parameter uncertainty is assumed to be norm-bounded. Nonlinear terms satisfy Lipschitz conditions. Random packet dropouts, time delays and quantization are taken into account in the feedback control problem simultaneously. Measured signals are quantized before being communicated. A logarithmic quantizer is utilized and the quantization error is regarded as sector-bounded uncertainty. The random packet dropouts are modeled as a Bernoulli process. A control law model which depends on packet dropouts and quantization is formulated. By Lyapunov-Krasovskii functional approaches, both state feedback and observer-based output feedback controllers are designed to ensure corresponding closed-loop systems asymptotical stability. Finally, two simulation examples are given to illustrate the effectiveness of the proposed methods.