H₂/H_∞ Control And Filtering For Time-varying Descriptor Systems

Time-varying descriptor system is a class of descriptor system whose parameters change with the measurable disturbance quantity in the system. Time-varying descriptor system has more extensive application value and prospect in the production, which has been applied in electric, aerospace, robot, etc. Due to control and filtering of system have been the focus of system control theory, the robust H₂/H_∞ filtering and control for a class of linear time-varying descriptor system was explored. The main contents are as followed. The robust H₂/H_∞ control for a class of linear time-varying descriptor system was explored. Firstly,the H∞ performance and asymptotic stable of the augmented the closed loop system is studied to make the H∞ bound within γ, the H2 performance and asymptotic stable of the augmented filtering error system is studied to make minimization the upper bound of H2 performance. And then based on the above, the sufficient condition which both satisfies H∞ performance index and H2 performance index, the asymptotic stable for the augmented closed loop system is presented. To reduce the design conservatism, the sufficient condition for the existence of robust H₂/H_∞ controller is proposed using parameter-dependent Lyapunov functions and LMI, which is shown in the form of bilinear matrix inequality. The robust H₂/H_∞ filtering for a class of linear time-varying descriptor system which is different from the first one was explored. Using the different parameter-dependent Lyapunov functions and LMI, the sufficient conditions for boundness of H∞ norm and for minimum of H2 norm of filtering error systems are presented respectively. And then based on the above, the sufficient condition which both satisfies H∞ performance index and H2 performance index, the asymptotic stable for the augmented filtering error systems is presented. On the basis of the robust H₂/H_∞ performance criterion, the sufficient condition for the existence of robust H₂/H_∞filtering is given. And the problem of filter design is converted into a parameter optimization problem with linear matrix inequality constraint.