Research On Robust Stability Of Sampled-data Control Systems With Time Delay

With the development of computer technology and semiconductor prices fall, the digital system has been widely applied to national defense, scientific research and other fields of public life etc.. Therefore, the sampled-data control systems as the basis of computer control,which requirements higher function. At the same time, time-delay widely exit in the actual project which will not only affect the performance of system, but also may cause the control system even instability. So, the robust stability analysis and design problems of the sampled-data control systems become a theoretical and engineering meaningful research problem.The robust stability of the sampled-data control systems with input delay are systematically studied in this paper. On frequency domain,based on the equivalent H?schema approach, the reason of conservativeness is pointed out, and then the frequency response method is studied for the systems. On time domain, in terms of Lyapunov function and a linear matrix inequality(LMI) method, the robust control design of the sampled-data systems with uncertain delay are systematically studied. Main works are summarized as follows:1. The robust stability analysis of sampled-data control systems with input delay is considered which using the equivalent H? approach. Based on the verification of the lifting technique approach in the former literature,the activity reason of conservativeness is pointed out. Then, using an discrete-time uncertainty to replace the continuous-time uncertainty of the sampled-data control systems,so the robust stability analysis for sampled-data control system is transformed into the robust stability analysis for traditional discrete-time control system,and thus the resulting conservativeness is reduced.2. As the conservativeness of the equivalent H? approach, a simple and intuitive robust stability analysis method -- the frequency response characteristics of the sampled-data system is provided. The sampled-data control system with input delay is regarded as the interconnection of two parts. One is the delay-independent and the other is dependent on the uncertain delay. Then the frequency response of the sampled-data control system with uncertainty delay is computed, and the robust stability is determined according to the frequency characteristic. The proposed method is not conservative. And the method for the average delay system is also suitable.3. The robust control design of the sampled-data systems with uncertain delay which based on the discrete uncertain sampled-data systems model is considered. The method is that the continuous-time uncertain plant of sampled-data system replaced by pure discrete-time systems,and then the robust controller design of uncertain sampled-data system is transformed into the robust stability and design problem of discrete systems with input delay.By using the Lyapunov function established the robust stability criterion of the sampled-data control systems, and given the design method of robust controller which based on the criterion with the parameterization of controller. The controller keeps the sampled-data systems robust stabilization and show good robustness for the perturbation of the structure.4. Robust stability problem of sampled-data control system with input delay is proposed .Unlike existing results, the controller treat input time-delay itself as an integer multiple of the sampling period, and then transform into the state delay continuous-time model. By using the so-called input-delay approach, a controller design technique for the input delay systems is provided. Based on Lyapunov-Krasovskii function method, and combined with the linear matrix inequality, the stability problem of the sampled-data system with input time delay is discussed, and given the design method of robust controller.