Robust Control Analysis For Uncertain Discrete-time Singular Systems

This dissertation mainly addresses the researches on robustness for a class of uncertain discrete-time singular systems. In the presence of a variety of disturbances, a necessary and sufficient condition for the robust stability is given. Through controlling the parameters and unmodeled disturbance in the system, a suitable state feedback controller would be designed . According to the method of regional pole placement and the H∞robust control theory, the controller that is designed would realize the system's stably.Singular system is an incomplete state of the system. This kind of systems includes the state perturbation. So when doing the theoretical analysis for a actually system and designing a viable controller, the singular state matrix― E should be fully considered. This paper is mainly using the state-space approach which has been researched to solve the problems of singular systems. As a premise, the system is wished to be regular, impulse-free and stability. Then the stability condition of an uncertain discrete-time singular system is discussed , and a designing method for the controller is given.The following points are mainly studied in this dissertation:1. Based on the regular state-space method of the regional pole placement, this paper addresses the necessary and sufficient conditions of the robust stability for a singular system with parameter perturbation.Continue to using the concept of Lyapunov stability, and place the system's poles in a unit circle with the center origin . Finally, in a form of linear matrix inequalities, a necessary and sufficient condition is proposed. At the same time, a suitable state feedback controller is also designed . This method can not only weaken the parameter disturbances and also can optimize the system's conservative.2. When there are external unknown disturbances, the robust H∞control theory is applied to get a necessary and sufficient condition to realize the system stability . Robust H_∞control theory is an optimal control method. So it can have a great inhibitory effect for the unmodeled disturbances. In this paper, the H_∞method is used to solve the problems of discrete-time singular systems with unmodeled disturbances . A necessary and sufficient condition is given here to guarantee that the controlled system is regular, stable and impulse-free. And for the given degree of decay―γ, the target system can be H_∞performance. Finally, a designing method for the controller is given in a form of linear matrix inequalities. The regional pole placement can not inhibit the external disturbances, but the H_∞method makes up its shortcoming . And a larger control range is got in this way. The LMI conclusion simplifies the solution process.3. Usually, an actually system has both the parameter and unmodeled disturbances simultaneously. According to the two points that are discussed above, the robust H_∞control method with a pole constraint is mainly researched. By the method , a designed controller can suppress both the external disturbances and internal disturbance effectively, and achieve optimal control for the regional pole placement. Also the system's conservative is further optimized .