H∞ Controller and Observer Design for Linear Systems with Point and Distributed Time-delays

A memoryless state feedback control law is developed such that the closed-loop system containing point and distributed time-delays is asymptotically stable and the H∞-norm of the transfer function from the disturbance to the controlled output is reduced to some predefined level. The feedback is obtained by solving a parameter-dependent linear matrix inequality. When the state variables are not available, an observer is built using a similar technique which generates an estimation of the state variables in order to implement the above state feedback. Copyright c © 2000 IFAC Keyword: Time-delay, Memoryless, H∞-Control, Observers, Linear Matrix Inequality (LMI).