Optimal Control Approach for Robust Control Design of Uncertain Time-delay Systems

This paper proposes an optimal control approach for the robust control design problem of the linear time-delay systems, which takes parameter uncertainties and state delay into account. It is shown that the robust control problem can be equivalently transformed into an optimal control problem with the amount of plant uncertainties indirectly reflected in the performance index. By introducing algebraic manipulations and appropriate uncertainty descriptions, a sufficient condition is derived under which not only the uncertain dynamical system can achieve stability, but can also reach the guaranteed level of performance. A suitable linear state feedback control law is characterized via Lyapunov stability theory to ensure quadratic stability and performance robustness of the closed-loop system.