H∞ Pinning Control of Complex Dynamical Networks Under Dynamic Quantization Effects: A Coupled Backward Riccati Equation Approach.

Abstract

In this article, a pinning control strategy is developed for the finite-horizon H∞ synchronization problem for a kind of discrete time-varying nonlinear complex dynamical network in a digital communication circumstance. For the sake of complying with the digitized data exchange, a feedback-type dynamic quantizer is introduced to reflect the transformation from the raw signals into the discrete-valued ones. Then, a quantized pinning control scheme takes place on a small fraction of the network nodes with the hope of cutting down the control expenses while achieving the expected global synchronization objective. Subsequently, by resorting to the completing-the-square technique, a sufficient condition is established to ensure the finite-horizon H∞ index of the synchronization error dynamics against both quantization errors and external noises. Moreover, a controller design algorithm is put forward via an auxiliary H2 -type criterion, and the desired controller gains are acquired in terms of two coupled backward Riccati equations. Finally, the validity of the presented results is verified via a simulation example.