Designing stabilising controllers and observers for uncertain linear systems with time-varying delay

A procedure to design the memoryless state-estimation feedback controller for uncertain dynamic systems with time-varying delay is presented. The uncertainties are time varying and are bounded. The design procedure involves solving two linear matrix inequalities. If there exist two positive definite matrices which satisfy these two linear matrix inequalities, then the asymptotic stabilisability of the closed-loop system is guaranteed. Furthermore, the state observer and control law can be constructed from these solutions. An example is given to illustrate the results