Study On The Dissipativity Of Generalized Delta Operator System

In practical systems, singular systems are a kind of more generalized systems than normal systems, which have been applied in more widespread extent, such as electronic networks, electric power systems, chemical engineering, mechanical systems and so on.Therefore, the study about singular systems is with more practical significance and promising application. Delta operator has an advantage in high frequency compared with traditional standard shift operator. Delta operator can solve the problem that discretization through shift operator may lead to parameter deviation in super high frequent condition.Moreover, it can maintain the stability of original continuous system. Dissipativity theory is an important section in control theory and modern electronic networks, which play a meaningful role in the study of stability and other characteristics of systems.This thesis mainly studies the problems of dissipativity analysis and dissipative control for singular delta operator systems. First, the problem of dissipativity analysis is considered for singular delta operator systems. By means of linear matrix inequalities,necessary and sufficient conditions are given to ensure a singular delta operator system admissible and strictly(Q, S, R)-dissipative. Furthermore, the problem of dissipative control is investigated for singular delta operator systems. The existence conditions and explicit expressions of a state feedback strict dissipative controller are presented through matrix inequalities, which can make the corresponding closed-loop system admissible and strictly(Q, S, R)-dissipative. By applying MATLAB-LMI toolbox, some numerical examples are provided to demonstrate the feasibility and effectiveness of the above theoretical results. Finally,based on the condition of admissibility in strict LMI form, we explore the issues about dissipativity analysis and control of singular Delta operator system. This paper shows us necessary and sufficient conditions of admissible and strictly(Q, S, R)-dissipative of singular delta operator systems in strict LMI form. Also, the sufficient condition of state feedback strict dissipative controller exists is in strict LMI form. By applying MATLAB-LMI toolbox, some numerical examples are provided to demonstrate the feasibility and effectiveness of the above theoretical results.