Robust quadratic performance for time‐delayed uncertain linear systems

In this paper, the analysis and control synthesis problems were studied for a general class of uncertain linear systems with variable time delay. It is assumed that the structured time‐varying parametric uncertainties enter the system state‐space description in a linear fractional fashion. The generic quadratic performance metric encompasses many types of dynamic system performance measure. In the context of delay‐independent stability, it was shown that the analysis and state‐feedback synthesis problems for such time‐delayed uncertain systems can be formulated equivalently as linear matrix inequality (LMI) optimization problems using the mechanism of full block multipliers. However, the solvability condition to output‐feedback problem was given as bilinear matrix inequality (BMI), which leads to a non‐convex optimization problem. A numerical example is provided to demonstrate the advantages of newly proposed control synthesis condition for time‐delayed uncertain systems over existing approaches.