The memoryless robust stabilization problem is studied for a class of uncertain linear dynamic systems with time-delyays in both state and control. The uncertain time-delay systems under consideration are described by state idfferental equations with timevarying unknown-but-bounded unceratin parameters. A suffficient condition for the existence of a memoryless robust controller is derived and two methods are presented for synthesizing robust control laws for uncertain time-delaysystems. One isto transform the robust control problem into a standared H∞ control problem via the equivalent system transfor mation, and thecontrol law can be obtainedby solving an algebraic Riccati equation (ARE). The other method is to transform the sufficient condition into a linear matrix inequality (LMI) problem and the control law can be obtained by solving the LMI. Finally, a numerical example ispresented to show the feasibility of the obtained results.

The robust H∞ control problem for time-varying uncertain linear systems with timevarying state and control delaysis considered. Based on the Riccati equationapproach, we design a robust H∞ linear time-invariant state feedback control law. Which stabilizes the system and resduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. A sufficientcondition for the existenceofthe robust H∞ controller is derived and two synthesis methods are presented for a robust H∞ control law to uncertain time-delay systems. One is to concription for the sufficient condition and the cntrol law can be obtained by solving an algebraic Riccati equation (ARE). The other method is to transform the sufficient condition into a linear matriz inequality (LMI) problem and the control law can be obtained by solving the LMI. A numerical example is presented to illustrate the obtained results.

The delay-dependent robust stabilization problem for a class of uncertain linear timedelay systems containing saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state. The delay is assumed to be constant bounded but unknown. New robust stability criteria and a suffcient condition for the existence of memoryless robust stabilizing control law are derived. The results depend on the size of the delay and are given in terms of several linear matrix inequalities (LMIs). A numerical example is presented to illustrate the obtained results.

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 H1 dynamic output feedback control laws by two equivalent linear time-invariant structural descriptions for the suffcient conditions, and the control law can be obtained by solving two Algebraic Riccati Equations (AREs). The other method is to transform the suffcient conditions into two L inear 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.

This paper mainly studies quadratic stabilizatio androbust Hx controller design fro linear uncetaindynamic systems with delayed state and control. Thepaper presents a static state feedback controller which stabilizes the plantand reduces the effect of thedisturbanceinput on the controlled output to prescribed levels for all admissible uncertainties. the sufficient conditions for quadratic stabilization witha Hx norm bound constraint are derived. The results can be regarded as an extension of existing resultsto robust Hx controller design forlinar uncertain dynamic systems with delayed state and control.