| Optimal control is one of important branches of modern control theory, and linear quadratic optimal control because one of the important theory, in the optimal control theory due to it widely applications in practice. For optimal solution of linear quadratic optimal control can be written as a unified analytic expression and can be represented as a simple state feedback controller which is easier for the calculation and realization in the engineering, so linear quadratic optimal control problem attracted many scholars of automatic control theory and technicians. In the latest half century, people studied many aspects of the linear quadratic optimal control problem like the structure, the character and method of designing the optimal state feedback controller which make it the most flourish part of the modern control theory.Consider that linear quadratic optimal problem is very important in control theory and has been used in practice widely, so the study of singular linear quadratic problem for descriptor systems has attracted scholars from home and abroad and already had a lot of excellent results.The linear quadratic performance for a descriptor system was well studied, and in [58] the problem studying a singular linear quadratic performance with the worst disturbance rejection for descriptor systems was came up. By using of the generalized inverses of matrices and semi-restricted equivalent transaction, in this thesis we replace the restricted condition with parameters in [58] by induce a rank constraint condition under which the existence and uniqueness of the worst disturbance and the optimal control-state pair can be obtained, the optimal control can be synthesized as state feedback, and all the finite eigenvalues of the closed-loop system are located on the open left-half complex plane. Since the verification of the rank constraint condition is easier than that find parameters to satisfy some hypothesis conditions, our method is available and convenient to the realization of engineering. |
