H_∞ Control Of Sampled-Data Control Systems

This dissertation is about the H_∞design for sampled-data control systems.Problems from the design by using the popular lifting technique are discussed andanalyzed, and new methods for the H_∞design of sampled-data systems areproposed.The lifting technique for sampled-data control systems is studied first, and theformulas for lifting computation are derived carefully. Because the computation israther complicated, a lifting algorithm is proposed by using MATLAB functions.The H_∞lifted plant and the corresponding L2 -induced norm can easily beobtained with the proposed algorithm.The lifting technique is then used for H_∞synthesis problems such as H_∞mixed sensitivity problem, robust stability problem and the disturbance attenuationproblem. It is pointed out that for the closed-loop sampled-data control system, thesystem norm is not preserved by the lifting as expected, i.e., there is a differencebetween the two norms. Two conditions A1 and A2 required for using the liftingtechnique in H_∞design are given, and it is pointed out that only the disturbanceattenuation design with no weighting functions or with weighting coefficients canmeet these assumptions, hence the practical application of the lifting technique inH_∞design is quite limited.The frequency response of sampled-data control systems is studied in detail.The presently accepted definition of the frequency response and the relatedcomputation with time-domain and frequency-domain lifting techniques are analyzedand discussed, and it is pointed out that the frequency response thus obtained isindeed the frequency response of the lifted system. Because the frequency responseof the system can not be preserved by lifting, the frequency response of the liftedsystem has nothing to do with the real frequency response of the sampled-datacontrol system.Notice that the signal channel of the system is really composed of twoparts——a continuous-time part and a discrete-time one, so a new method forcomputing the frequency response of the sampled-data control system is proposedaccording to the special structure of the sampled-data control system. This method iswith clear physical meanings, and the result can be checked by various methods. TheL2-induced norm of the system can also be obtained from the frequency response...