On delay-dependent robust H∞ control of uncertain continuous-and discrete-time linear systems with lumped delays

This paper develops a Linear Matrix Inequality (LMI) approach to the robust H_∞ control problem of uncertain continuous-and discrete-time linear time-invariant systems with time-delay in the state vector and control input. The main results provide sufficient delay-dependent conditions for the control problem, where the explicit size of the time delay plays a crucial role for the closed-loop stability. The solutions that are found for the H;_∞ control problem are less conservative, when compared to other approaches.