The Stability And Variable Structure Control Of Uncertain Distributed Parameter Systems With Time-delays

Distributed parameter systems have been an important research branch, based on the permeation of functional differential equations with partial differential equations naturally. 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.As it is considered above, the paper is concerned with the property problem of uncertain distributed parameter systems with time-delays based on the functional differential equation stability theory and variable structure control method. The research situation and results of the paper are as follows:1.The research meaning of the paper is explained by introducing the topic background, including the history and the present development condition of stability,oscillation and variable structure control theory in respect of distributed parameter systems with time-delays, and the study progress on 2-D discrete system.2.The exponential asymptotical stability is analyzed for the uncertain distributed parameter system with time-delays.The sufficient condition of exponential asymptotical stability is obtained for the uncertain distributed parameter systems with time-delays by using the auxiliary functional method, and combining with Divergence theorem and Poincare inequality, and some processing techniques of time-delays and uncertain terms in functional differential equations.3.The oscillation is analyzed for the uncertain distributed parameter system with time-delays. The sufficient condition of the system oscillation is obtained on the Hurwitz angular domain [0, k] by using Green formula and the technique of inequality, and some processing technique of the uncertain terms.4. The stabilization is analyzed for the uncertain distributed parameter system with time-delays.A sufficient condition of stabilization is obtained for the system by constructing even type Lyapunov function, and employing the linear matrix inequality method, and some processing techniques of time-delays and uncertain terms in functional differential equations. A numerical example is given to illustrate the feasibility of the method in the section.5.A class of uncertain distributed parameter system with time-delays is researched by using the variable structure control method. A variable structure controller without time-delays is designed. On sliding switch surface, the invariant characteristic of uncertain variables of the sliding mode control system is analyzed. And the estimated time which the system's trajectories reach the sliding mode in is given. The effectiveness of the proposed design method is illustrated by a numerical example.6. The stability is analyzed for the discrete 2-D time-delays systems with interval coefficient. A sufficient condition of the stability is obtained for the systems by using the technique of inequality and discussing three cases of the interval coefficient. The effectiveness of the proposed method is illustrated by a numerical example.At last, the full paper is summarized, and some greatly significant research problems are proposed.