The Stability Analysis And Observer Design For Classes Of Nonlinear Systems

In this paper, the reduced-dimension design of a novel discrete-time linear systems with disturbances and discusses its simple applications and observer design and stabilization for a class of nonlinear neutral type systems with time-delays is discussed are researched. In addition, observer design and stabilization for a class of nonlinear neutral type systems with time-delays is are discussed. The subject of separate system state variables dimensionality reduction method, combining sliding mode variable structure control method of linear matrix inequalities are the main research methods. The corresponding simulation examples are given in order to illustrate the feasibility and effectiveness of some results in the paper.The main contents summed up as the following five sections.1. The definition and development of discrete-time systems are reviewed. As preparatory knowledge, the review of research for nonlinear systems in the past few decades and its current development is presented. This leads to the work to be done in this paper.2. This section investigates the reduced-dimension design of a novel discrete-time linear systems with disturbances and discusses its simple applications. In order to reduce the dimension of the linear systems, firstly, the original state variables are divided into dominant and non-dominant state variables, a reduced dimension model is obtained and it only contains the dominant state variables. Secondly, a sufficient condition is derived for the design of reduced dimension observer using this reduced dimension linear model. Finally, a numerical simulation example is given to illustrate the feasibility of the results in the paper.3. In this section, observer design and stabilization for a class of nonlinear neutral type systems with time-delays is discussed. Firstly, an observer is given for the system. Secondly, a sufficient condition of the stable is presented for the closed-loop system of the system and the error system by using some linear matrix inequalities and Lyapunov second method based on the linear state feedback of the system. Finally, a numerical example is given to demonstrate the effectiveness and feasibility of the proposed method.4. In this section, the observer-based sliding mode control (SMC) problem is investigated for a class of nonlinear delay systems. First, the linear sliding surface is defined, a new stability condition is proposed for the sliding mode dynamics. Second, a sliding mode observer is designed, based on which an observer controller is synthesized by using the SMC theory combined with the reaching law technique and the feedback compensation controller. And a sufficient condition of the asymptotic stability is proposed in terms of LMI for the overall closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability problem is also discussed, making sure the reachability of the sliding surfaces defined in both the state estimate space and the state estimate error space. Last, a numerical example is given to illustrate the effectiveness and feasibilityof the proposed design scheme.5. All the results of this paper are summed up in this part. And the further study plan and the outlook are given.