Asymptotic Tracking Controlfor Linear Descriptor Systems

Descriptor system theory is one of the dynamic system theory which formed and developed in the1970s. Descriptor system more general than the normal system, and has a wider application background. In recent decades, people give descriptor systems more widespread concern. Not only some theoretical results of the normal systems have been successfully applied to the descriptor systems, and some new results of descriptor systems themselves have also been developed. In this paper, descriptor linear time-invariant systems are involved, discussions of the problems about descriptor systems tracker designning are raised, the main achievements in two aspects:Firstly, model-reference tracking control of descriptor linear model system is considered. We extent the problem of the model-reference tracking for common linear systems to descriptor linear systems and give the design method for it. The controller consists of two parts: the state feedback stabilization controller and compensator. The controller meets three linear equations and based on the parameter solution of generalized Sylvester matrix equation, we give the absolute parametric form of the controller and basis on this, an effective algorithm for the designing of model-reference tracking control is given. Combined with specific example, we further demonstrate that the proposed method is simple and effective.Secondly, we studied the tracking control of descriptor linear robust model. We extend our problem from tracking control for descriptor linear model to that for robust descriptor linear model with parameters perturbation. It is mainly through the search of optimal parameters, that we minimize the impact of the uncertainty of the tracking error and at the mean time, we give an efficient algorithm for the design of robust model tracking control, and one specific example is given.