SUBOPTIMAL H-INFINITY AND OPTIMAL LQG CONTROLLERS FOR CONTINUOUS-TIME TRANSPORT-DELAY SYSTEMS

A polynomial-based solution is presented to the continuous-time LQG and H infinity control design problems for systems with transport delays. Polynomial solutions to these problems are not currently available in the literature. The multivariable LQG problem is first considered and solved using a Wiener type of analysis. The polynomial solution to this problem is then presented for the scalar case and this result is then used to derive the H infinity optimal controller. In this latter case an approximation must be introduced but this does not affect the stability of the solution. The H infinity and LQG controller structures for stable plants resemble a Smith predictor. However, the solution is also applicable to open-loop unstable systems. The solution of the H infinity problem in both generic and non-generic cases is obtained. A detailed example is presented of the solution procedure for both of these cases. The system description and cost function are quite general.