Sliding mode observers for infinitely unobservable descriptor systems

This thesis describes the use of a class of sliding mode observers for state and unknown input estimation for descriptor systems. Existing work has shown that suitable scaling of the equivalent output error injection term of the sliding mode observer can yield an accurate estimation of the unknown input. Work can also be found on the development of the sliding mode observer for the descriptor system, a variation of the regular state space which can better represent certain systems. The existing sliding mode observer design for the descriptor system requires global observability which can be restrictive. In this thesis, new methods are presented to achieve state and unknown input estimation using the sliding mode observer for a class of descriptor systems that is not globally observable. Reformulation is key to the approach and is made with the forethought of capitalising on the ability of the sliding mode observer to estimate unknown inputs. The reformulation is done by treating certain states as unknown inputs to obtain a fictitious system that is globally observable. Then using the existing work which assumes global observability, the sliding mode observer can be designed for the fictitious system to effectively estimate the states and unknown inputs of the original descriptor system that is not globally observable. It is crucial for the number of outputs to still be in excess of the number of unknown inputs in the course of formulating the fictitious system, as doing otherwise will violate one of the fundamental conditions that governs observer designs. While the idea of reformulation generally applies, each method (which is discussed in a separate chapter) employs a unique technique of reformulating the descriptor system, building up from a simpler technique to a more complex one. All the methods will be accompanied by their respective necessary and sufficient conditions in terms of the original system matrices so that the feasibility of applying any of them can be easily determined. The effectiveness of the schemes will then be verified using numerical examples.