Robust H∞ control of time-varying delay systems with probabilistic uncertainties

Until now, only sufficient conditions have been available for robust H_∞ control of linear time-varying delay systems. Then, an interesting problem is: if the existing sufficient conditions are all failed for a system, how can we design an H_∞ controller for it? We solve this problem by considering probabilistic uncertainties in the system model. The system matrices have parameter uncertainties described by given probability distributions. The system state includes a delay whose magnitude is upper bounded by a constant. First, a randomized algorithm is proposed for designing a controller that makes sure both asymptotic stability and a prescribed H_∞ performance level are satisfied for the resulting system over the uncertainty domain in a probabilistic sense. Then the probability of H_∞ performance is used to quantify the capability of the designed controller. Finally, we perform a convincing simulation to clarify the developed approach.