Research On Sampled-Data Control System Based On Input Delay Approach

With the rapid development of microelectronics and digital signal technology,digital system has been widely applied to many fields, for instance, the nationaleconomy, the compilation of national defense construction and scientific experi-ments, etc. Therefore, computer control has been developed into a core of auto-mation technology. Sampling controller design is a key problem of sampled-datacontrol theory, which provides theoretical guidance for the computer control. Asis known to all that the actual system is usually most complicated, it may appeara variety of the combination of complex characteristics which consists of uncer-tainty, infinite dimension, nonlinearity, stochastic, strong coupling, and so on.The coexistence of continuous signal and discrete signal is not only the outstan-ding characteristics of sampled-data control system, but also a difficulty ofsampled-data system analysis and design as well. At present, the design methodsof sampling controller mostly aim at lifting technique and jump system method.In this dissertation, however, the input delay approach is adopted to studysampled-data control problem. Time domain state space model of the sampled-data system, robust stability, robust controller design and guaranteed cost controlhave been deeply researched. In the framework of input delay approach, thesampled-data control system will be transformed into the continuous system withinput delay. On the basis of reference, summary and study of the existingresearch results at home and abroad, with the need of the practical application, bymeans of guaranteed cost control theory, the sampled-data control theory, Lyapu-nov stability theory, and Linear Matrix Inequalities (LMI) method, the subjectfocuses on guaranteed cost control for the uncertain time-delay linear sampled-data control system and the uncertain time-delay nonlinear sampled-data controlsystem; exponential stability for uncertain linear systems and nonlinear time-delay disturbance system; stochastic sampled-data control for uncertain nonlinear disturbance system, etc. Concrete work for this topic can be summarized asfollows:Firstly, we considered guaranteed cost sampling control under the conditionsof a class of uncertain systems with time-variable delay. The uncertainty of thesystem is norm bounded uncertainty. In the framework of input delay approach,the sufficient condition of the existence of the uncertain time-variable delaylinear system optimal robust guaranteed cost sampling controller and the contro-ller design method were discussed and given by way of an application to Lyapu-nov stability theory and LMI method.Secondly, guaranteed cost sampled-data control problem was considered for aclass norm bounded uncertain time-variable delay nonlinear system in this disser-tation. Based on the Lyapunov stability theory and the input delay approach, thesufficient conditions are given for the existence of the uncertain time-variabledelay nonlinear system guaranteed cost sampling controller in the form of LMI aswell as the controller design method. At the same time, we also got the robustoptimal guaranteed cost sampling controller design method and numericalexamples illustrate the effectiveness of the proposed method.Thirdly, the exponentially stable problem of sampled-data control system wasinvestigated with the known upper bound for sampling interval in this disserta-tion. According to the input delay approach, sufficient conditions of exponentialstability were given in the form of LMI.Fourthly, the problem of constant sampling control and variable sanplingcontrol for uncertain exponentially stable systems were considered respectivelyin this dissertation. With the Lyapunov stability theory, in the framework of inputdelay approach, sufficient conditions of exponential stability were given in theform of LMI.Fifthly, for the nonlinear time-delay system with known sampling intervalupper bound, the constant sampling and variable sampling respectively wereconsidered in the paper. In the framework of input delay approach, sufficientconditions were given for exponentially stable system and satisfied the givenperformance index.Sixthly, the problem of stabilization and robust H_∞control were studied forsampled-data systems with two sampling priods. By introducing a stochastic variable satisfying a Bernoulli distribution and using the input delay approach,the stochastic sampling system is transformed into a continuous time-variabledelay system with stochastic variable and time-variable delay. By adopting thefree-weighting matrices approach, sufficient conditions are proposed to guaranteethe closed-loop system is robust mean-square exponential stability and satisfiesH_∞performance index.