Abstract: With the design technique of robust controller and the design idea of robust quadratic stabilization controller, robust control of the closedloop system was
carried out to eliminate the adverse effects of delay factors and uncertainties on the actual system. By constructing a new Lyapunov functional, the author proposed design method of delaydependent and delayindependent controller based on linear matrix inequality. The results show that the designed state feedback controller can make the closedloop system satisfy the performance requirements within the allowable range of uncertainty, and reduce the sensitivity of the system. Numerical results show that the obtained results are more universal and can be applied to the nonstandard systems with uncertain timevarying delay.

Key words: robust control, delaydependent, linear matrix inequality (LMI), singularly perturbed system, delayindependent, timevarying delay, LyapunovKrasovskii functional