T-S Model-based Relaxed Reliable Stabilization of Networked Control Systems with Time-varying Delays under Variable Sampling

This paper investigates the reliable stabilization problem for a class of nonlinear networked control systems (NCSs) under variable sampling with variant state and network delays. An equivalent continuous-time uncertain fuzzy system with both state and input time varying delays, subject to possible actuator faults, is derived based on the Takagi-Sugeno (T-S) model and the input delay method. In order to obtain much less conservative results for the delay system transformed, a more relaxed stabilizability condition of a delay-free T-S system and a tighter bounding lemma for some derivative terms of the constructed functional are utilized for closed-loop stability determination of the NCS under variable sampling. Delay-dependent fault-tolerant stabilization conditions formulated in terms of linear matrix inequalities for the possibly faulty network-based system are derived by employing a novel Lyapunov-Krasovskii (L-K) functional, which makes good use of the information of both the lower and upper bounds on the two interval delays. An example is provided to show the validity of the obtained results.