Background: The networked control systems are becoming progressively more significant
and have many outstanding advantages compared to traditional point-to-point control systems. T-S
fuzzy systems are nonlinear systems described by a set of If-Then rules. Especially, the combination
communication networks with feedback control loops for fuzzy systems are worthy of being
investigated, such as network-induced time delays, and control.
Methods: Owing to existing network-induced random delays of the forward and feedback
communication links in a direct-drive linear control system, we use two homogeneous Markov chains to
express the delays. For the stability analysis, the new Lyapunov function and the free-weighting matrix
inequality technique are used.
Results: A new stability criterion is obtained, and the controller can be computed in terms of linear
matrix inequalities (LMIs). The new criterion is less conservative for a new non finite-sum term is
introduced in the Lyapunov-krasovskii functional, which brings some adjustable slack variables into the
criterion, and can be efficient use of the networked delay information.
Conclusion: The new stability criterion is shown to be effective and efficient by the numerical
examples. It improves the stability theory of networked control systems and T-S fuzzy systems.