The Stability And Sliding Mode Control Of Distributed Parameter Systems And It(?)-type Stochastic Systems

Distributed parameter systems have been become an important research branch, based on the permeation of functional differential equations with partial differential equations naturally. Now, there are two main methods to research the distributed parameter system. One is the direct analysis method; the other is the C 0?semigroup method. In practical control systems, the system could not exclude the influence of state time-delays, parameter perturbation or external disturbances, and distributed parameter systems are of infinite dimensions and high complexity. All of these bring up great difficulty for the analysis and design of the system. Therefore, it is necessary to design a simple and easy method, which is fit for the engineering designer.In practice, stochastic factors exist objectively, and the system described by the method of certain systems may lose some characteristics. If the control method of certain system theories is taken to control some practical systems, the practical system will deviate from expected results seriously. Therefore, the stochastic factor has to be taken into account in the description of systems. For example, in respect of some questions of the signal transfer in communication, the diffuseness of pollution source in environment pollution, the measure of material information in ocean engineering and so on, the stochastic modeling must be constructed to analysis and research these problems. Therefore, the modeling of stochastic systems is of important practical meanings as to engineering problems. The so-called stochastic system is differential dynamic systems of the time process, which points to describe stochastic factors.As it is considered above, the paper is concerned with the property problem of distributed parameter systems and It(o|^) type stochastic systems. The main work and research results of the paper are as follows:1.Firstly, the paper introduces the topic background, including the history and the present development condition of sliding mode control theories in respect of distributed parameter systems and It(o|^) type stochastic systems. Based on this foundation, the research meaning of the paper is explained. 2.The exponential asymptotical stability analysis is carried out for the uncertain distributed parameter system with time-delays. By making use of the auxiliary functional method and combining with Green formula, Poincaréinequality and some processing techniques of time-delays and uncertainties in ordinary functional differential equations, the inequality analysis method of lumped parameter systems are successfully extended to the stability analysis of the uncertain distributed parameter system with time-delays. In addition, the sufficient condition of asymptotical stability for the uncertain distributed parameter systems with time-delays is obtained.3.The sliding mode control of the uncertain distributed parameter system with time-delays is discussed. Under certain conditions, the sliding mode controller is designed. On sliding switch surface, the invariant characteristic of uncertain variables and the stability of the sliding mode control system are analyzed.4.Under the meaning of mean square, the exponential asymptotical stability of the parameter uncertain It(o|^) type stochastic system with multi-time-varying delays is studied. By making use of the Lyapunov function and Ito? differential formula, the algebraic criteria of exponential stability are given in mean square. At last, the feasibility of the result in the paper is illustrated by an example.5.The sliding mode is studied in respect of the uncertain It(o|^) type stochastic system with time-varying delays. Moreover, the variable structure controller is constructed directly. By using Ito? differential formula, matrix inequality and stochastic differential theory, the sub-reachability of the sliding mode is proved. At the end, a sufficient condition of the sliding mode stability is derived by using the extended Halanay's inequality in mean square. A simulation example is given to illustrate the feasibility.In the last section, the main work in the paper is summarized and the sliding mode control problem of distributed parameter systems and stochastic systems are prospected .