Nonstandard H∞Control And Zero Placement Of Descriptor Systems

As an important branch of modern control theory, the descriptor system has beenwidely studied. In recent years, the descriptor system which is based on state feedbackmethod has achieved fruitful results by using state space method. State space method,however, is not the only method which is used to study descriptor systems. As anotherkind of research method, frequency domain method has the advantages of physicalintuition and convenience of design. At the same time, not all state variables can beeasy to obtain in practical application. Hence, the descriptor system which is based onoutput feedback method has important theoretical and practical value.The main contents of this paper summarized as follows:1. The descriptor system is studied on non-standard H∞output feedback controlproblem. Compared with standard H∞output feedback control problem, thedescriptor system which this chapter studied consists of unstable or irregular weightfunctions, at the same time, it does not include the item parameter D. The appropriateoutput feedback controller is deduced by using the generalized Sylvester equations,generalized Riccati equations and spectral radius condition. The closed-loop system isallowed, and the infinite norm of the closed-loop transfer function is less than a givenconstant gamma which is greater than zero. Finally, a numerical example is used toprove the correctness.2. The output tracking input control problem of the descriptor system is studiedbased on output feedback method, the input signal is generated by the reference model.The tracking problem is studied by two ways: without considering the performanceindex and considering the performance index. The simulation results verify theeffectiveness of the control methods in the end.3. Output feedback stabilization and zero placement of the descriptor system areinvestigated. First of all, parametrization of the output feedback controllers by doublycoprime factorization approach is used to stabilize the descriptor systems from thestate-space perspective. Then, from the angle of the frequency domain, the zeroplacement problems of the closed-loop system are discussed in the condition that theclosed-loop system is admissible, and the zero placement method is proposed to design different zeros. Finally, the numerical examples are given to show theeffectiveness of the method.