Output regulation for all-pole and minimum phase LTI

Abstract

In this thesis, the problem of enabling the output of a system to track the reference signals and reject the disturbances created by the same exogenous system is considered. This problem is widely known as Output Regulation Problem. Firstly, we propose a method for all-pole LTI systems by using relative degree property and then we apply the same method for minimum phase LTI systems along with some modifications. In order to obtain controllers for a minimum phase LTI case, the system is converted into an all-pole system by employing the inverse system as the first part of the controller. Then using the method that we used in all-pole cases, we obtain the second part of the controller. Combining these two controllers gives us an overall controller which solves the output regulation problem. This method for LTI systems is then extended to all-pole and minimum phase LTV systems. However, in order to apply the same methodology we have to make some assumptions on LTV systems. For minimum phase cases, the normal form is obtained by applying certain Lyapunov transformations and then minimum phaseness is defined in accordance with the normal form. Furthermore we show that, similar to minimum phase LTI cases, pole / zero cancelations occur between the inverse system and the original system in minimum phase LTV cases. The method that we develop depends on analytical calculation of the controller and gives a certain degree of freedom to change the transient behavior of the system by only changing some controller parameters.