Improved robust H∞ stability analysis and stabilization of uncertain systems with stochastic input time‐varying delays

International audienceThis 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