Controller design for delayed systems via an LMI-based stability test and convex optimization

A new sufficient condition is given for stability of an observer based control scheme for unstable linear systems with input and output delays. By means of a Ljapunov-Krasovskii functional, the stability test is reduced to a feasibility problem for a set of linear matrix inequalities (LMI). The test is utilized for a stable affine parametrization of the closed-loop system, which is the basis for the application of numerical convex optimization to the design of robust controllers. This will be further illustrated by means of an example problem, the control of an open-loop unstable tubular reactor.