Analysis and design on hybrid dynamical systems: stability, control and filtering

Electronic full text of this thesis published publications are unavailable. See print copy in SpArk for full text.In order to control the behavior of a system, it is necessary to capture the salient system features in a mathematical model. Dynamic systems are intrinsically difficult due to their system complexities, the challenge of measuring various parameters and also the uncertain and/or time-varying parameters. The development of systematic methods for efficient and reliable design of such complex control systems is a key issue in control technology and industrial information. It is currently of high interest to control engineers, computer scientists and mathematicians in research institutions as well as in many industrial sectors. In practice, a large class of physical systems has variable structures subject to random changes. These may result from abrupt phenomena such as component and interconnection failures, parameters shifting, tracking, and the time required to measure some of the variables at different stages. Systems with this character may be modeled as hybrid ones, that is, to the continuous state variable, a discrete random variable called the mode, or regime, is appended. The mode describes the random jumps of the system parameters and the occurrence of discontinuities. Such a system model is useful particularly since it allows the decision maker to cope adequately with the discrete events that disrupt and/ or change the normal operation of a system significantly, by using the knowledge of their occurrence and the statistical information on the rate at which these events take place. This thesis is based on my research into hybrid dynamical systems. Most of this research has been conducted through theoretic studies with experiments (either numerical or practical examples) to verify the obtained results, which has great potential for practical applications. Therefore it is wholly consistent with the mission of the university from which I seek this degree award.Thesis (D.E.) (Research by Publication) -- University of Adelaide, School of Electrical and Electronic Engineering, 2015