Delays could arise as well from inherent physical phenomena and also couldbe intentionally introduced for some design consideration in order to eliminate orreduce the e?ect of time delay. As a source of degradation in control e?ciencyand instability of control system, delays can not be ignored. Thus, it has been anactive and complicated research area since the 1960's. Although plenty of resultsabout time delay system control have been achieved, most of them are induced tosome di?cult problem and not solved in essence. For discretetime systems withdelays, one might tend to consider augmenting the system and convert a delayproblem into a delayfree problem. While the augmentation approach generallyresults in higher state dimension and thus high computational cost, especiallythe systems under investigation involves multiple delays and the delays are large.For continuoustime systems, the delayed problems can in principle be treatedby the infinitedimensional operator Riccati equations which are di?cult to beunderstood and implemented.The intrinsic time delayed properties of system may lead to measurementdelays, but the time delays in measurement equations of this thesis are alwaysresulted from the signal transmission processing of the sensors which is used toobserve. System with time delay in measurements arise in the optimal controlmodel with delays, input/output model and ?exible robot model. The time takenin the filtering and processing of the sensory data for the required control forcecalculation and the transmission of the control force to the actuator or the timetaken by the actuator to produce the required control force may result in inputdelays. System with input delay arise in many engineering fields such as aircraftcontrol and network control.In this thesis, we considered two problems which are discussed for discretetime case and continuoustime case, respectively. One is measurementfeedbackHâˆžcontrol for systems with delayed measurement(s), and the other one is thetracking control for systems with multiple input delays. The main contributionsof this thesis are listed as follows.First, we proposed a new method which solved the problems of measurementfeedback Hâˆžcontrol with delayed measurement(s) by reorganized innovationanalysis approach in Krein space. Based on Krein space theory, the problems...
