As a special class of nonlinear systems, the research of Lipschitz nonlinear systems gives an impetus to nonlinear control, and these discussions enrich the research of control theory. Over the past few decades, many scholars have studied of controller and filter design problems for the Lipschitz nonlinear system, and some relevant results are available. It should be noted that many of the existing research results are based on the theory of Lyapunov asymptotic stability, and the system characteristics analysis is within an infinite-time range. But an asymptotic stable system is likely to have some bad transient performance, and will cause some bad effects; these will not meet the requirements of industrial production, such as the overshoot amount is too large, and the maximum overshoot or oscillation sharp occurs. In addition to study the steady state performance in the Lyapunov sense, people also concern about that the systems should satisfy some transient performance requirements. Based on this, Dorato put forward a new concept of finite-time stability, i.e., short time stability, and then the concept of finite-time control problems have been widely analyzed and used.The main work of this dissertation investigates Lipschitz nonlinear systems, including such systems subject to uncertainties, time delays and nonlinearities. The research contents mainly relate to finite-time controller design, finite-time filter design, the observer-based robust controller design, etc. The relevant design approaches can be reduced to a feasible problem of linear matrix inequalities (LMIs). The main works of this dissertation are divided into three parts, and the main contents are as follows:(Ⅰ) The robust finite-time controller design for Lipschitz nonlinear systems:This section studied the robust finite-time controller design problems for a class of Lipschitz nonlinear systems. By constructing a proper Lyapunov function, a sufficient condition is given so that the closed-loop control system is finite-time bounded and satisfy the given H∞control index. The relevant results can be obtained by solving a set of LMIs. Simulation results demonstrate the validity of the proposed approaches.(Ⅱ) The robust finite-time passive filter design for Lipschitz nonlinear systemsBased on the finite-time boundedness and passive control theory, this section studied the robust finite-time passive filter design problems for a class of Lipschitz nonlinear systems. By constructing a proper Lyapunov function and using LMIs techniques, a sufficient condition is given such that the closed-loop control system is finite-time bounded and satisfy the given passive control index. The relevant results can be described as an optimization one.(Ⅲ) The observer-based robust finite-time passive controller design for Lipschitz nonlinear systemsThis section studied the observer-based robust finite-time passive filter design problems for a class of Lipschitz nonlinear systems. By constructing a proper Lyapunov function and using LMIs techniques, a sufficient condition for the solvability of the finite-time robust passive controller and observer problem is given.In the last part, the conclusions and research prospects are given. Furthermore, some further research work and existing issues for Lipschitz nonlinear systems are also pointed out. |