The use of Lyapunov's direct method in obtaining regions of asymptotic stability of non-linear autonomous systems is well-known. This thesis is an investigation into the optimization of some function of these systems over different classes of Lyapunov functions. In Chapter 2 bounds on the transient response of two systems are optimized over a subset of quadratic Lyapunov functions and numerical work is carried out to compare several bounds. Zubov's equation is the subject of Chapter 3. The non-uniformity of the series-construction procedure is studied analytically and a new approach is made to the solution of the equation by finite difference methods. Chapters 4, 5 and 6 have a common theme of optimizing the RAS over a class of Lyapunov functions. Chapter 4 is restricted to optimal quadratics which are investigated analytically and numerically, two algorithms being developed. An optimal quadratic algorithm and a RAS algorithm are proposed in Chapter 5 for high order systems. Extensions are made in Chapter 6 to optimal Lyapunov functions of general degree and relay control systems and systems of Lur'e form are considered.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:472478 |
| Date | January 1973 |
| Creators | Shields, Derek N. |
| Publisher | Loughborough University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://dspace.lboro.ac.uk/2134/35647 |
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