Positive Real Control And Dissipative Control Problem For Singular Systems

In recent years, positive real is always a popular research area in control theory,and strict positive real is playing a very significant role in the system. Dissipativity asa very important concept in system and control theory is also researched extensively.Dissipativity and PR are widely applied in researches of system stability, robustcontrol and nonlinear control. In the area of uncertain discrete time singular system,the researches of dissipativity and PR are not common, thus this paper describes someresearches that have been done in this area. And the results will be summarized asfollows（1）The research background and development of singular system are introduced,and the object of study in this paper uncertain discrete-time singular system model isput forward. Then,for the current situation and development prospects of the study ofPR and dissipativity, a brief introduction is given.（2）By the use of generalized quadratic stability and extended strict positive realcharacters of discrete time singular system, the sufficient conditions for the uncertaindiscrete time singular system to be quadratic admissible and strict positive real aregiven. Through introducing the augmented system, the analysis and design of theuncertain discrete time singular system are translated to be discussed under thecondition of discrete time singular system. At last, the design method of statefeedback controller and output feedback controller is presented, and the validity ofthe method is proved to be true by numerical examples.（3）Through using the sufficient and necessary conditions for the discrete timesingular system to be admissible and ESPR, the equivalence relation between theESPR and strictly dissipativity of the normal system of uncertain system and theaugmented system of the nominal system are established. And then the robustdissipativity analysis of the uncertain discrete time singular system is converted toprove that its augmented system is strictly dissipative. At last, the design method ofrobust dissipative controller is proposed by introducing the state feedback controllerto the uncertain discrete time singular system. Then, numerical examples are employed to verify the method.（4）Summary of the major work and thoughts is made, then, the future trends thatrelated studies other singular system in positive real and dissipative field are listed.Simulations results of the main design scheme demonstrate that the providedcontrol strategy can lead to expected achievements, so the control algorithm ispractical.