Probabilistic Design of Networked Control Systems With Uncertain Time Delay

Networked control systems (NCSs), where control loops are closed through a real-time network, have been adopted in many application areas. Examples include manufacturing plants, automobiles, aircraft, and spacecraft. However, the insertion of a real-time network introduces time delays due to time-sharing of the communication media. The network-induced delay can degrade the performance of an NCS, and can even destabilize the system. Due to its random nature, in this paper, we apply the promising probability robust control approach to handle the network-induced delay, which is modeled as an uncertainty governed by a probability distribution function. With considering both stability and performance of NCSs in the stage of control design, we propose the synthesis condition of ℋ∞ state-feedback control of NCSs. It is formulated as a set of linear matrix inequalities with uncertain parameter present in the the state-space data. The ellipsoid randomized algorithm is applied to solve the matrix variables and design a probabilistic robust controller. A numerical example is given to demonstrate the probabilistic design method for NCSs.