Generalized System Of Sub-optimal Control

Since 1970s singular systems were raised, as it was used widely in aerospace system, power system, robot system, biological system, chemical system, ecnomic system and circuit system, and so on, so it provoked interest of many scholars. The study of its theory has been made a great progress. Some conclusions of linear system have been extended to singular systems. There have been many excellent results related to linear quadratic optimal control problem, but few in suboptimal control problem of singular systems. For the design of pratical projects, we do not need find accurate optimal regulator, we only need to find the regulator which satisfied the desigin requirement, so it is necessary to reserach suboptimal control problem. In recent years, nonregular singular systems were widely discussed, but few results about suboptimal control problem.In this thesis, we analyse the exisiting results of nonregular singular systems and suboptimal control problem of singular systems. Using semirestrictied equivalent transformations and Moore-Penrose generalized inverses of matrices, we replace the restricted condition of parameters in [Journal of Shandong University,2006,41(2):74-77] by some rank conditions of coefficient matrices. A suboptiaml control-state pair is constructed, which ensures the performance of the close-loop system is within certain range. The suboptiaml control can be synthesized as state feedback, and all the finite eigenvalues of the close-loop are located on the open left-half complex plane. The method is easier to caculate the solution, so it is convenient to applications in enginearing.