Exponential stability analysis and impulsive tracking control of uncertain time‐delayed systems

In this paper, we study exponential stability and tracking control problems for uncertain time‐delayed systems. First, sufficient conditions of exponential stability for a class of uncertain time‐delayed systems are established by employing Lyapunov functional methods and algebraic matrix inequality techniques. Furthermore, tracking control problems are investigated in which an uncertain linear time‐delayed system is used to track the reference system. Sufficient conditions for solvability of tracking control problems are obtained for the cases that the system state is measurable and non‐measurable, respectively. When the state is measurable, we design an impulsive control law to achieve the tracking performance. When the state information is not directly available from measurement, an impulsive control law based on the measured output will be used. Finally, numerical examples are presented to illustrate the effectiveness and usefulness of our results.