Lm2-stable digital-control networks for multiple continuous passive plants.*

A constructive method is presented in which Lm2-stability can be guaranteed for networked control of multiple passive plants in spite of random time varying delays and data dropouts. The passive plants are interfaced to a wave variable based passive sampler (PS) and passive hold (PH) which allows a passive digital control network to be constructed. A power junction is used to facilitate the interconnection of multiple passive plants and passive digital controllers. The power junction preserves passivity by guaranteeing that the overall power input to the system is greater than or equal to the power leaving the system. There are numerous ways to implement the power junction including the averaging power junction and the consensus power junction which are studied in this paper. In particular, a detailed steady state analysis is provided which relates the corresponding controller inputs to the plants outputs. The construction of our digital control network is completed by interconnecting the digital controllers to an inner-product equivalent sampler and zero-order hold (IPESH) which allows us to prove Lm2-stability.