Control And Analysis Of Stochastic Uncertain Sampled-Data Systems

Stochastic factors generally exist in the dynamic systems. For the cases when thestochastic factors can be ignored, the dynamic stochastic systems are treated as the deter-ministic systems. However, it is necessary to deal with the system with stochastic factorsas a stochastic system when the accuracies of the design requirements are high. Withthe development of the computer technique and the gradual maturity of the digital signalprocessing, the computer technique, which can realize complex algorithms, provides theeffective methods for the realization of the stochastic system theory. In computer controlsystems, the single sampling rate is frequently an idealized sampling method. However,when the stochastic sampling strategy is employed in some dynamic systems, the sam-pling rate, data redundancy and computational complexity will be decreased which makeit possible to control these systems, for instance the phased array radar monitoring andtarget tracking system. For present, the results on the stability analysis and synthesis forthe systems with stochastic sampling are concerning the deterministic systems, and thisfield research for the uncertain systems is a hot spot of the system science and controlscience. The emphasis in this thesis is focused on studying the problems of stability andperformance analysis, state-feedback controller design, observer-based output-feedbackcontroller design and H∞filtering for the stochastic uncertain sampled-data systems. Andthe thesis presents analysis and synthesis methodologies of the sampled-data control andfiltering for the stochastic systems in the unified framework. Parts of the developed theo-ries is applied to the networked control systems. The main contents are as follows:The problems of stabilization and robust H∞control are investigated for sampled-data systems with stochastic sampling. Under the case in which two sampling periodsalternately appear with a given occurrence probability, the stochastic sampling system istransformed into a continuous time-delay system with stochastic parameters by introduc-ing a variable satisfying a Bernoulli distribution and employing the input-delay approach.This idea is further extended to the case with multiple stochastic sampling periods. Anew Lyapunov-Krasovskii function approach is developed to establish the mean-squareexponential stability of the closed-loop system by using the free-weighting matrices ap-proach. Based on this, the design procedure for stabilization controllers is proposed for the closed-loop system. When considered norm-bounded parameter uncertainties in thestochastic systems, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an H∞performance. On base of this, thecontroller design problem with closed-loop H∞performance is also solved. The resultsin this part are more advanced than the results with single sampling and the advantages lieespecially in the reduced conservatism owing to the fact the stochastic sampling is takeninto consideration. The idea of H∞controller design is further applied to the networkedcontrol systems.The problem of the H∞filtering is studied for the sampled-data systems withstochastic sampling. State estimate is one of the important issues in the control fields.The filtering error system is established for the filter system with stochastic sampling, inwhich the sampler exists between the the measured output and the filter input. By meansof LMIs approach, H∞filter is designed such that the filtering error system is exponen-tially stable in the mean square, and the H∞performance satisfies a prescribed level.Similarly, taking into account the stochastic sampling can obtain less conservative resultsthan the systems with single sampling rate in the H∞filter design.The problem of sampled-data stabilization for Ito? stochastic systems with intervalparameter uncertainties and nonlinear term. The interval parameter uncertainties are char-acterized by a matrix bound and the non-linearity is assumed to satisfy the boundednesscondition. Based on this, a Lyapunov-Krasovskii function approach is developed to es-tablish the mean-square exponential stability of the closed-loop system and propose thestate-feedback controller design. Moreover, with the consideration that the state variablesare difficult to measure, the observer-based controller design for the nonlinear stochasticsystems is proposed such that the system is robustly exponentially stable. The stabilityanalysis problem for that system is not solved until the input delay approach is employedto deal with the sampled-data systems.The problem of stabilization is investigated for the discrete-time systems withstochastic sampling. In this closed-loop feedback system, the plant is discrete systemand two sampling frequencies alternately exist in the input of the controller. The mean-square stability condition of the closed-loop system is established and a procedure fordesigning stabilization controllers has been formulated in the form of linear matrix in-equalities. This study shows that taking into stochastic sampling in continue systems or discrete systems can reduce the conservatism.The H∞control problem is studied for the networked control systems with stochas-tic sampling. The network topology structure is CAN network owing to the fact thatnetwork-induced delay is always less than the sampling period and event driven is sup-ported in CAN network. The controlled plant is a mechanical system consisted of twocars, a spring and a damper. According to the aforementioned idea, sufficient conditionsare obtained, which guarantee the mean-square exponential stability of the system withan H∞performance. Moreover, an H∞controller design procedure is then proposed. Thesimulation shows the validity of the control strategy and have less conservatism. This partconstitutes an attempt of applying stochastic sampling strategy to practical engineeringproblems, which extends the stochastic systems theory and provides a design idea for thestudy of networked control systems as well.