Single-Input Systems with Arbitrary Relative Degree

This chapter examines single-input systems with arbitrary relative degree. It considers the situation when the actuator state is measurable. The control objective is to design a control strategy to compensate for the system uncertainty as well as actuator delay to ensure all the signals of the closed-loop system are bounded. The chapter then employs the well-known Kreisselmeier-filters. It also looks at the more complex situation of the unmeasured actuator state. Again, Kreisselmeier-filters are employed to virtually estimate the unmeasured ODE state. Finally, the chapter summarizes the stability of the ODE-PDE cascade system (in which the actuator state is unmeasured), before illustrating the proposed scheme.