Study On Robust H_∞Control And Filtering For Nonlinear Singular Systems With Time Delay

With the development of science and technology, Many scholars of control researchfield found a great many of the actual systems, such as the economic systems, cranesystems, robotic systems and electrical power network systems, etc. At the same time,these models generally have time-varying, time-delay, uncertainty, dispersion, nonlineardisturbances links, structural complexity and high dimensions, which makes it a greatchallenge, great difficulty and necessity for the study of the uncertain nonlinear singulartime-delayed system. Uncertain nonlinear singular time-delayed systems are composed ofby algebraic constraints, time-delayed differential equations and nonlinear uncertainties,which have a wide range of applications in various engineering systems, especially inlarge-scale grid control, large chemical systems, aerospace, wireless transmission lines,economic and artificial neural network systems. Therefore, the study of robust H-infinitycontrol and filter design problems for some uncertain nonlinear singular time-delayedsystems is with very important theoretical value and practical application significance.In this thesis, we investigate the robust H-infinity control and filter design problemsfor several classes of uncertain nonlinear singular time-delayed systems, the main workare generalized as follows:1) The robust H-infinity controller design problem for a class of uncertain nonlinearsingular systems with time delay both in the state equation and output equation is studied.Based on linear matrix inequality (LMI) method, we construct some new Lyapunovfunctions and a robust H-infinity controller. Using Matlab LMI Control Toolbox, we get aparameter expression of the robust H-infinity controller. Finally, a numerical example isgiven to show the validity and feasibility of the proposed method.2) Based on a new delay bounded real lemma, we discuss the problem of robustH-infinity controller design for a class of discrete-time nonlinear uncertain singularsystems with time delay both in the state equation and output equation. we design thememory robust H-infinity controller of such nonlinear uncertain singular discrete-timedelayed closed-loop systems which are asymptotically stable and satisfy the robustH-infinity performance index. Finally, a simulation example is given to verify the validityand applicability of the proposed method.3) The robust H-infinity filter design for a class of nonlinear uncertain singular systems with time-varying delay is investigated. Based on linear matrix inequality (LMI)method, we construct some new Lyapunov functions and a robust H-infinity filter. wedesign the robust H-infinity filter of such nonlinear uncertain delayed filtering errorsingular systems which are asymptotically stable and satisfy the robust H-infinityperformance index. Finally, two numerical examples are given to illustrate the validity andscientificalnessof the proposed method.4) The robust H-infinity filter design for a class of nonlinear uncertain discrete-timesingular systems with time delay is investigated. Based on linear matrix inequality (LMI)method, we construct some new Lyapunov functions and a robust H-infinity filter. UsingMatlab LMI Control Toolbox, we get a parameter expression of the robust H-infinity filter.Finally, the numerical simulation is given to verify the validity and practicality of thedesigned method...