Passive Control For A Kind Of TS Fuzzy Descriptor Systems  Posted on:20091005  Degree:Doctor  Type:Dissertation  Country:China  Candidate:Y Zhang  Full Text:PDF  GTID:1118360308479185  Subject:Control theory and control engineering  Abstract/Summary:  PDF Full Text Request  Dissipative theory plays an important role in the analysis and control research of systems. The implication is that there exists a nonnegative energy function (namely store function) such that the energy consumption of a control system is always less than the supply rate of the energy. The passivity is an important part of the dissipativeness. It takes the product of the input and the output as the supply rate of the energy, which embodies the attenuation property of a system under bounded exogenous input. In fact, the stabilization theory based on Lyapunov function can also be explained in view of the passivity. Therefore, the passivity is a further abstraction of the stability. When investigating the stabilization of a system, a Lyapunov function is alwagys needed. According to the present literatures, this process can be converted into constructing a store function that makes the system passive.The research on passive control for TS fuzzy descriptor system is still in preliminary stage. Many unsolved problems need to do. In this paper, by using the advanced matrix theory and the linear matrix inequality (LMI) technique, the problem of passive control and nonfragile Hâˆžcontrol for a kind of TS fuzzy descriptor system is studied under the framework of Lyapunov stability theory, which is motivated by the linear descriptor system theory and advanced robust control theory. The main contributions are as follows:(1) The passive control problems are considered for TS fuzzy systems and TS fuzzy descriptor systems. Passive control is firstly discussed for TS fuzzy systems and TS fuzzy descriptor systems without uncertainty, and the conditions for the closedloop systems to be admissible and passive with dissipationÎ·are proposed in the cases of state feedback controller, observerbased feedback controller and dynamic output feedback controller. Then robust passive analysis and control are discussed for TS fuzzy systems and TS fuzzy descriptor systems with normbounded uncertainties. The design of observebased controllers is presented for the closedloop systems to be generalized quadratically stable and passive with dissipation 77.(2) The passive control problems are discussed for TS fuzzy systems and TS fuzzy descriptor systems with timedelay. As for the timedelay fuzzy systems, by using of the Lyapunov technique and introducing the LyapuniovKrasovskii functional, the existence conditions of state feedback, observerbased feedback and dynamic output feedback passive controllers with their design methods are derived in terms of linear matrix inequalities, such that the closedloop systems are admissible and passive. The results gained in this paper can be generalized into the case of systems with normbounded uncertainties.(3) The nonfragile passive control problems are considered for TS fuzzy systems and TS fuzzy descriptor systems. The main idea is to design nonfragile controller such that the closedloop system is robustly stable and passive with dissipationÎ·. The nonfragile state feedback controller is designed firstly to guarantee the relative performance of the systems, and then nonfragile observerbased controller with the perturbations in both the control gain and observer gain is discussed for TS fuzzy descriptor systems. The observer gain perturbations are in both the additive form and multiplicative form. Moreover, the existence conditions and design methods are presented in terms of LMI. The passive control problem of uncertain TS fuzzy systems with timedelay is investigated. The nonfragile controller is designed to guarantee the passivity of the systems.(4) The nonfragile Hâˆžcontrol problems are considered for TS fuzzy systems and TS fuzzy descriptor systems. By virtue of the property of membership function, the Hâˆžcontrol conditions are generalized with nonfragile state feedback controller.As to the conclusions obtained in the paper, simulation examples are presented to show the effectiveness of the proposed methods.
 Keywords/Search Tags:  TS fuzzy descriptor systems, passive control, Lyapunov stability theory, linear matrix inequality (for short LMI), H_∞control, state feedback controller, observer, dynamic output feedback controller, nonfragile control  PDF Full Text Request  Related items 
 
