Pearson, J. Boyd2009-06-042009-06-041992Bamieh, Bassam Abbas. "Analysis and robust control of hybrid continuous/discrete time systems." (1992) Diss., Rice University. <a href="https://hdl.handle.net/1911/16545">https://hdl.handle.net/1911/16545</a>.https://hdl.handle.net/1911/16545Hybrid Continuous/Discrete Time Systems are systems in which one part evolves in continuous time and another in discrete time. Important examples of such systems are digital (sampled-data) control systems, in which a continuous time plant is controlled by a digital controller using sample and hold devices. Traditionally, such systems have been discretized and treated as discrete-time systems thereby ignoring their continuous time (or inter-sample) behavior. The traditional approach is not applicable in modern theories of robust control such as ${\cal H}\sp\infty$ or $\ell\sp1,$ where for continuous time plants it is more natural that plant and signal uncertainties are given in continuous time. Therefore, to pose robust control problems with sampled-data controllers, one needs to consider the continuous time behavior of these systems. The continuous time behavior of sampled-data systems is in general periodically time varying. A new framework is developed for continuous-time periodic systems which has many of the useful qualities of the time invariant theory such as transforms and constant state space realizations. The framework is based on a lifting technique which establishes a strong correspondence between periodically time-varying systems in continuous time, and certain types of infinite dimensional time-invariant systems in discrete time. The utility of this framework is shown by posing and providing exact and constructive solutions to both the ${\cal H}\sp\infty$ and the $\ell\sp1$ sampled-data control problems, where the performance specifications are given in terms of continuous time uncertainties. A natural generalization is given for the ${\cal H}\sp2$ problem in the case of time-varying systems. This is used to pose the ${\cal H}\sp2$ problem for sampled-data systems, and a complete solution is also obtained.109 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ElectronicsElectrical engineeringThesisThesis E.E. 1992 Bamieh