Dynamic output feedback stabilizing control for linear time-varying uncertain systems with delayed state and control

A robust stabilizing problem for linear time-varying uncertain systems with delayed state and control is studied when the full state can not be measured. An observer-based dynamic output feedback controller is derived to quadratically stabilize the linear time-delay system with norm-bounded uncertainty. A sufficient condition of robust output feedback stabilizability of a system is presented, then the sufficient condition is transformed into a linear matrix inequality (LMI) problem and the control law can be obtained by solving two LMIs. Finally, a numerical example is presented to illustrate the obtained results.