Robust Stability And Control Of Linear Singular System

In this dissertation, robust stability and robust control are presented for linear singular systems with time-delay. Criteria are given for robust stability and robust stabilization of singular systems. Robust controller, robust H∞filter and robust dynamical output feedback controller are designed under the limited properties. We provide the criteria of robust stability for the uncertain neutral singular systems and designed the robust H∞filter is by the theory of singular systems.The main contributions of this paper are as follows:(1) The time-delay dependent robust stability and robust stabilization control problem for linear singular systems with time delay are discussed. Based on Lyapunov-Krasovskii function, a time-dependent condition for the robust stability is obtained by using integral inequality and "0" matrix method. The controller which can guarantee the closed loop system with regular and impulse-free robust stability via the state feedback is designed. A numerical example illustrates the feasibility and effectiveness of the designed controller.(2) The time-delay dependent robust H∞control problem is studied. A time-dependent criterion for the robust H∞properties is derived by using appropriate uncertain parameter Lyapunov-Krasovskii function and quadratic integral inequality. A sufficient time-dependent condition for the robust H∞ state feedback is given. A numerical example is given to illustrate the feasibility of the designed controller.(3)The design problem of full order H∞filter for continuous singular system is addressed in order to design satisfactory full order H H∞filter with regular and impulse-free filter error dynamics. Lyapunov-Krasovskii functional and quadratic inequality method was used to get Hx time-delay criterion of filter error dynamics. A sufficient condition of robust H∞filter existence of singular system is provided. A numerical example is given to verify the effectiveness and practicability of the design method.(4) The robust H∞dynamical output feedback control problem for uncertain singular systems is considered. Based on Lyapunov-Krasovskii function and linear matrix inequalities, the robust time-delay dependent dynamical output feedback controller is designed. The controller can make the closed loop system is regular and impulse-free and guarantee the H.r properties which restraint the disturbance are satisfied. A numerical example is given to verify the effectiveness and practicability of the design method.(5) The time-delay dependent robust stability for uncertain neutral singular systems is discussed. Based on Lyapunov-Krasovskii function, a time-dependent sufficient condition for the robust stability is gained by using integral inequality and "0" matrix method. The sufficient condition is provided by linear matrix inequalities. A numerical example demonstrates the feasibility of the theorem.(6) The design problem of full order H∞filter for uncertain neutral singular system is addressed in order to design satisfactory full order H,r filter with regular and impulse-free filter error dynamics. Lyapunov-Krasovs-kii functional and quadratic inequality method was used to get H∞time-delay criterion of filter error dynamics. A sufficient condition of robust H∞filter existence of uncertain neutral singular system is provided. A numerical example is given to verify the effectiveness and practicability of the design method.