Research On Problems Of Non-fragile Control And Filtering Of Sampled-data System With Long Time-delay

With rapid development of digital technology, sampled-data control technology has been extensively applied to welding industry, aeronautics and astronautics, signal processing, earthquake prediction and so on. Combing sampled-data control technology and non-fragile control theory yields non-fragile control theory of sampled-data system. In sampled-data system, sampling plant is provided with time-delay and time-delay is longer than a sampling period, which is called by sampled-data with long time-delay. Research content of such system may be divided into stability analysis, design of non-fragile controller, observer and filtering. Aimed to time-delay’s processing approach, there are usually two approaches, one is distributed direct approach, the other is concentrated augmented approach. In-depth research and discussion of sampled-data system with long time-delay are presented by making use of two afore-mentioned approaches. This work mainly includes:Firstly, in the framework of discrete domain, sampled-data system with long time-delay model is established. In the process, relation of system’s time-delay and sampling period is taken fully into account, Consequently, State’s long time-delay is transformed into two successive state time-delay of discrete-time system. Two successive state time-delay is processed by concentrated augmented approach and distributed direct approach, and then Lyapunov stability theory and LMI technology is combined with LMI technology, and stability condition of sampled-data system with long time-delay are presented. Specially, applying distributed direct approach, free weighting matrix and congruent transformation matrix are introduced, so that computational burden of stability’s sufficient condition is less, and based on solving linear matrix inequality, designed approach of non-fragile controller is provided.Secondly, according to sampled-data system with long time-delay model which has been established, whose pole is located in a round domain inside unit circle. By linear transformation, a round domain inside unit circle is in conversion to unit circle. Thereby,D-stability of system is transformed into equivalent asymptotically stable problem, and then, by constructing quadratic Lyapunov functions and solving linear matrix inequality, analysis approach of D-stability and designed approach of non-fragile controller is presented.Thirdly, towards sampled-data system with long time-delay model which has been established, when system’s state is unknown and partly known, the problem of analysis and synthesis can’t be solved by state feedback. Thus, observer is designed to reconstruct state. Based Lyapunov function, stable analysis and synthesis of observe error system is researched. Solving linear matrix inequality, nonlinear term of LMI is in conversion of linear term, thereby, designed approach of non-fragile observer and controller are presented, which ensure H∞performance index of system is satisfied.Finally, according to sampled-data system with long time-delay model which has been established, whose state is unknown and whose noise is non-gaussian bounded, state estimation is used. By constructing filtering error system, and combining Lyapunov stability theory and linear matrix inequality technique, stable condition of filtering error system is presented and H∞and passive performance index are satisfied. By solving linear matrix inequality, designed approach of non-fragile H∞filter and non-fragile passive filter are proposed respectively.The simulation examples in every issues of sampled-data system with long timedelay verify the effectiveness and feasibility of the proposed results and methods.