Passivity and Passification for Networked Control Systems

• Authors: Huijun Gao;Tongwen Chen;Tianyou Chai
• Venue: SIAM Journal on Control and Optimization
• Year: 2007

This paper investigates the problems of passivity analysis and passification for network-based linear control systems. A new sampled-data model is first formulated based on the updating instants of the ZOH (zeroth order hold), where the physical plant and the controller are, respectively, in continuous time and discrete time. In this model, network-induced delays, data packet dropouts, and signal measurement quantization have been taken into account. The measurement quantizer is assumed to be logarithmic, and the network-induced delays are assumed to have both a lower bound and an upper bound, which is more general than those assumptions used in the literature. The key idea is to transform the sampled-data model into a linear system with two successive delay components in the state. Then, by using a Lyapunov-Krasovskii approach plus the free weighting matrix technique, a passivity performance condition is formulated in the form of linear matrix inequalities (LMIs). Based on this condition, two procedures are proposed for designing passification controllers, which guarantee that the closed-loop networked control system (NCS) is passive. Finally, two illustrative examples are presented: one shows the advantage of introducing the lower bound of transmission delays and shows how much the quantization behavior affects the passivity performance; the other illustrates the applicability and effectiveness of the proposed passification results.