Robust H∞ control for time-delay networked control systems with probability constraints

In this study, the probability-guaranteed H_∞ control of networked control systems (NCSs) with time-varying networked-induced delays is addressed. The time-varying delays are modelled as polytopic uncertainty by a new approximation method based on real Jordan form. The system uncertainty lies in a parameter hyper-rectangle box which can shrink, i.e. the probability can be less than one with a better disturbance attenuation level. By the uniformity principle and the one-to-one correspondence between the time delays and the vertices of polytopic system, a sufficient condition for the NCS to achieve prescribed performance with a given probability is derived. The controller synthesis problem is also proposed to meet the probabilistic requirement by solving a set of bilinear matrix inequalities iteratively. A uniform distribution is assumed for all the delays and thus the maximal probability guaranteeing the given performance can be calculated.