In this thesis, the application of state space theory to the analysis and synthesis of electrical networks is considered. The state equations consist of a set of first order linear differential equations of the form dx/dt = Ax + Bu where u is the input vector and x the,state vector. The problem of setting up these equations for the case of RLC active networks, containing controlled generators, is examined. A topological approach is taken which gives a method for finding, by inspection, the maximum number of state equations, the maximum order of complexity, for a class of networks. An algebraic approach is also taken. A method is suggested for forming the equations and a way of determining the order of complexity given. It is shown that, with very small restrictions the problem of finding the maximum order of complexity can be greatly simplified. Necessary and sufficient conditions are given for the network to possess a unique solution. The relationship between the concepts of system theory and network synthesis are considered. In particular, the relationship between the order of complexity and the degree is considered. The problems associated with poles at infinity are considered and a more general transformation suggested for generating all equivalent irreducible realizations for systems with poles at infinity. The use of state space theory for network synthesis is reviewed and the problems of active network synthesis are considered.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:623111 |
| Date | January 1968 |
| Creators | Purslow, Eric John |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/16047 |
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