This paper investigates the robust stability analysis and state feedback controller design of networked control systems (NCSs). A stochastic network-induced delay in given interval with known lower and upper bounds is considered. Therefore, the NCS is modeled as linear system with probabilistic time-varying delay distribution. Then, the Lyapunov-Krasovskii functional (LKF) is formulated using probabilistic informations of both lower and upper bounds of the time-varying network-induced delay, and Wirtinger-based integral inequalities are used to estimate the accuracy of the resulting time derivatives and also to reduce conservatism by introducing some new cross terms. Afterwards, stability condition based on [Formula: see text] disturbance attenuation level is expressed in terms of a set of linear matrix inequalities (LMIs), and Finsler’s lemma is used to relax it by adding slack decision variables and decoupling the systems matrices from those of Lyapunov-Krasovskii. This procedure makes the state feedback controller design as simple as a variables change. Finally, a maximum allowable upper bound of the network-induced delay and state feedback controller gains are calculated by resolving the above relaxed LMIs’ convex optimization problem. Practical numerical examples are provided to validate the proposed approach; the results show that the negative effects of the unpredictable network-induced delays are compensated and the stability of NCSs with high disturbance attenuation level is guaranteed. A comparative study with other results in recent researches is also given and the superiority of the proposed method in terms of robustness and conservatism reduction is shown.

This article focus on the robust H ∞ stability analysis and controller design for a class of uncertain and disturbed continuous-time systems with input time-varying delays characterized by stochastic Bernoulli distributions. First, robust H ∞ stability conditions for linear continuous systems with interval input time-varying delays is investigated. A delay-distribution-approach is considered to reduce the conservatism of the stability conditions from the convenient selection of a Lyapunov-Krasovskii functional (LKF), which considers both the lower and upper bounds of the stochastic time-varying delay to derive new delay-dependent H ∞ stability conditions in terms of linear matrix inequalities (LMIs). Then, derived from the proposed stability conditions, LMI-based conditions for the design of stabilizing robust H ∞ delayed state feedback controller are proposed. Finally, five numerical examples are considered to show the effectiveness of the proposed stability analysis and controller design conditions, in comparison to previous related results.

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