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Probabilistic-Robust Optimal Control for Uncertain Linear Time-delay Systems by State Feedback Controllers with Memory

In this paper, a new method is developed for robust control of uncertain linear time-delay systems with feedback control whose gain matrix is time-varying. In contrast to the available linear matrix inequality (LMI)-based techniques for stabilizing linear time-invariant (LTI) uncertain time-delay systems where the feedback controller is chosen memoryless with a constant gain matrix, the feedback control has memory over time in the new proposed LMI-based technique. In addition, two new constraint removal approaches are proposed to solve this problem as a chance-constrained optimization problem. The proposed approaches are developed such that the closed-loop systems are robustly asymptotically stable in the presence of uncertainties. In an illustrative example, it is shown that the proposed techniques can successfully stabilize a linear second-order time-delay system with a time-varying feedback control. It is also shown that the proposed constraint removal approaches are more efficient in comparison to the current approaches for approximating chance-constrained problems.