Pole Generalized Delta Operator Systems Configuration And Observer Design

Singular systems are a kind of more generalized dynamic systems, which can provide more accurate descriptions of practical systems than normal systems do, such as robot systems, biological systems, aerospace and electronic networks, and so on. After40years of development, the essential features of singular systems have been studied deeply, and fruitful results have been achieved.In the1980’s, delta operator method was put forward to give a unified description of continuous systems and discrete systems. It can avoid the numerical instability problem of shift operator method at high-speed sampling rates, and also has better finite word length performance than shift operator does.In this paper, we study the problems of pole assignment and observer design for singular delta operator systems. Firstly, the delta operator is introduced to the discrete model of a singular continuous system, and thus the delta operator model is established for the singular continuous system which will tend to the corresponding singular continuous system when the sampling period tends to zero. Secondly, based on the relation between singular delta operator systems and singular discrete systems, the problems of controllability analysis and observability analysis are considered for singular delta operator systems, and the corresponding results are given. Then from the relations between controllability and pole assignment, observability and observer design, the problems of state feedback pole assignment and observer design are investigated for singular delta operator systems, and the corresponding design methods are provided. In the end, some numerical examples are presented to verify the feasibility and effectiveness of the results in this paper.