Optimization Design Of Robust Quantized Filter/Controller For Uncertain Discrete-time Systems

With the rapid development of the digital controller and the network-based controltheory, the quantized phenomenon has received more and more concerns. This is mainlybecause that, the quantized effect is not considered in the traditional design, which usuallyleads to the reduction of system performance and even destruction of the system stability.In order to solve this problem, many approaches have been proposed. And there are twomain strategies: one is the so-called dynamic quantized method, which depends ondynamically modifying the parameters of quantizer so that the quantized system isasymptotical stable and satisfies the given performance. However, this policy does notconsider the minimum number of quantization levels, and leads to complex analysis.Different from the former method, another method named the static quantized approach isbased on the fact that in the practical case, the communication channel is bound. Then, byusing the sector bound approach, the above related quantized error influence can bechanged to the norm-bounded uncertain issue. Therefore, we can use the mature robustcontrol theory to design controller/filter to solve such problem.On the basis of the merit of the static quantizer, this dissertation is mainly to give theLMI （Linear Matrix Inequality） method to design filter/controller to mitigate the quantizederror effect in the communication channel between the filter/controller and plant.Meanwhile, we have also considered some optimal control performance indicators: H∞performance,GH₂performance and peak to peakperformance. Generally, thedesign contents and methods can be concluded as follows: for the system outputquantization, the quantized error can be transformed into a norm bounded uncertainty viausing the sector bound approach. Then, take the H∞performance andGH₂performanceinto consideration, the filter design conditions can be obtained by using relaxed lemmasand effective matrix transformation techniques. On the other hand, this paper considers thecase that both the system output and controller input are quantized. Via using two sectorbound approaches, such quantization can be changed to LFT （Linear FractionalTransformation） uncertainty without loss of conservatism. Similar to the above filterdesign, the peak to peakperformance is considered to design optimal dynamic outputfeedback controller which can mitigates the quantized error effect and meets someprescribed control requirements. Finally, the numerical simulations are given in everychapter to demonstrate the effective of the proposed approaches.In the end, the results of the dissertation are summarized and further research problems are pointed out.