Robust H control for linear time-varying uncertain time-delay systems via dynamic output feedback

Abstract

This paper focuses on the analysis and synthesis problem of robust H control for a class of linear time-varying uncertain systems with delayed state and control when the full states cannot be measured. A dynamic output feedback controller is given to quadratically stabilize the linear time-delay system with norm-bounded uncertainty and reduce the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. Sufficient conditions for the existence of a robust H dynamic output feedback control law are derived and two synthesis methods are presented for a robust H dynamic output feedback control law to uncertain time-delay systems. One method is to construct robust H dynamic output feedback control laws by two equivalent linear time-invariant structural descriptions for the sufficient conditions, and the control law can be obtained by solving two Algebraic Riccati Equations (AREs). The other method is to transform the sufficient conditions into two Linear Matrix Inequalities (LMIs) and the control law can then be obtained by solving two LMIs. A numerical example is presented to illustrate the proposed methodology.