Stability Analysis And H_∞ Analysis Of Piecewise Linear Deltaoperator Systems

Delta operator theory is introduced to the control field in the twenty-eighties. It is a bridgeto contact the continuous systems and discrete systems, which has been received considerableattentions on the majority of scholars in the field of control and made a series of importantresearch results. In addition, Delta operator theory plays an important role in the applications,such as system modeling and identification, computer control, high-speed digital signal process,rapid sample data and so on.It is well know that piecewise linear systems is not only a powerful tool of the generalnonlinear systems and uncertain systems, but also represent a large class of actual engineeringsystems. In the past two decades, as computing technology, the analysis and synthesis ofcontrol theory for piecewise linear system has been received much attention in theory andpractical research. Therefore, the study for piecewise linear system has a profound theoreticaland wide range of practical prospects.With respect to the characteristics of the Delta operator system and the piecewise linearsystems, this paper will consider the piecewise linear Delta operator systems. The contents ofthis thesis are given as follow:Firstly, the sufficient conditions that can render the stability of the piecewise linear Deltaoperator systems will be given by using linear matrix inequality. Based on the S-procedureprogram, we give the less conservative sufficient conditions of stability for the system;Next, Based on the linear matrix inequality approach, we consider the H_∞analysisproblem for the piecewise linear Delta operator systems. In the real system, the systemdisturbance rejection capability needs to be considered, H_∞theory provides an effective wayto deal with this problem.The obtained results in this thesis are a foundation for the study of synthesis H_∞problems and uncertain problems of piecewise linear and Delta operator systems.