Scheduling control of the temperature profile of a catalytic rod

We address the problem of temperature-profile scheduling control on a catalytic rod model. Galerkin technique can be successful to reduce the infinite-dimensions temperature profile equation into a finite-dimensions equation. Then, we can get the state stability of the infinite-dimensions temperature profile equation through analysing the related finite-dimensions equation. To overcome the difficulty that the obtained reducing system is difficult to design controller because of its nonlinearity. Combing the Lyapunov analysis technique, a stability criterion with sufficient conditions is given and the controller gains are designed by linear matrix inequality approach. In the end, how to design schedulable controller gains is shown in the section numerical example simulation.