Passive Control For A Kind Of T-S Fuzzy Descriptor Systems

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 T-S 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 non-fragile H∞control for a kind of T-S 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 T-S fuzzy systems and T-S fuzzy descriptor systems. Passive control is firstly discussed for T-S fuzzy systems and T-S fuzzy descriptor systems without uncertainty, and the conditions for the closed-loop systems to be admissible and passive with dissipationηare proposed in the cases of state feedback controller, observer-based feedback controller and dynamic output feedback controller. Then robust passive analysis and control are discussed for T-S fuzzy systems and T-S fuzzy descriptor systems with norm-bounded uncertainties. The design of observe-based controllers is presented for the closed-loop systems to be generalized quadratically stable and passive with dissipation 77.(2) The passive control problems are discussed for T-S fuzzy systems and T-S fuzzy descriptor systems with time-delay. As for the time-delay fuzzy systems, by using of the Lyapunov technique and introducing the Lyapuniov-Krasovskii functional, the existence conditions of state feedback, observer-based feedback and dynamic output feedback passive controllers with their design methods are derived in terms of linear matrix inequalities, such that the closed-loop systems are admissible and passive. The results gained in this paper can be generalized into the case of systems with norm-bounded uncertainties.(3) The non-fragile passive control problems are considered for T-S fuzzy systems and T-S fuzzy descriptor systems. The main idea is to design non-fragile controller such that the closed-loop system is robustly stable and passive with dissipationη. The non-fragile state feedback controller is designed firstly to guarantee the relative performance of the systems, and then non-fragile observer-based controller with the perturbations in both the control gain and observer gain is discussed for T-S 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 T-S fuzzy systems with time-delay is investigated. The non-fragile controller is designed to guarantee the passivity of the systems.(4) The non-fragile H∞control problems are considered for T-S fuzzy systems and T-S fuzzy descriptor systems. By virtue of the property of membership function, the H∞control conditions are generalized with non-fragile state feedback controller.As to the conclusions obtained in the paper, simulation examples are presented to show the effectiveness of the proposed methods.