Roubust Optimal Control Of T-S Fuzzy Descriptor System With Constraints

In recent years, generalized T-S fuzzy system has been widely used in control theory, circuit, economic, mechanical and other areas. Therefore, it has important realistic significance to study generalized T-S fuzzy system. In practice control systems, various kinds of constraint conditions are widespread. In order to meet the high performance requirements of control system, greater control actions are needed so that contradictions between the high performance requirements and meeting the constraints generate. Only consider the system performance without considering the constraints, control actions will exceed the bounds greatly. Therefore, constraints must be considered in controller design.Firstly, the robust stability of uncertain T-S fuzzy singular systems with constraints is studied in this paper and a robust stability analysis method is proposed. Based on the generalized Lyapunov stability theory and linear matrix inequality(LMI) technique, a sufficient condition for unconstrained T-S fuzzy singular systems robust stability is got. And then find an elliptic domain where the initial state to change the constraints into a group of LMI bindings by using elliptic invariant domain method and S-Procesure lemma. Finally a sufficient condition for system robust stable and satisfying the time-domain constraints is given. On this basis, the optimal control method dealed with a kind of constrained generalized T-S fuzzy systems optimal control is discussed. Taken the output energy of the system as the optimal performance indicators, the upper bound of the initial state x0ETPx0 is got such that indicators depend on the upper bound and take it as the upper bound of the elliptical invariant domain. The optimal control of T-S fuzzy systems can be realized by minimizing this upper bound of system. Then the sufficient condition statisfied the constraints can be obtained by using the elliptical invariant domain method.Finally, robust H∞control of uncertain T-S fuzzy singular systems is considered. When there are external interferences, a H∞control strategy which applies the double elliptic domain method to find the sufficient condition satisfied the time-domain hard constraints is proposed. An elliptical domain where the initial state is found. Then look for conditions satisfying a certain inequalities in the closed-loop system. Meanwhile, under the condition of assuming that the energy of the external interferences are less than some boundary, another elliptical domain which contains all possible states of systems is determined. Thereby, sufficient condition depended on the elliptical domain to meet time-domain hard constraints is obtained.