Date of Award
Doctor of Philosophy
Electrical and Computer Engineering
Two new algorithms are developed to determine estimates for the domain of attraction of the equilibrium x = 0 of nonlinear systems described by systems of equations of the form x(' )=(' )f(x). One of these algorithms utilizes quadratic Lyapunov functions while the second algorithm makes use of norm Lyapunov functions. Analysis of the results obtained for specific examples demonstrates that these two algorithms yield estimates for the domain of attraction which are comparable to those obtained by existing methods; however, the present algorithms appear to be significantly more efficient than the existing algorithms. The relationship between the eigenvalues of the Jacobian and Lyapunov matrices is established, and then based on this relationship and computational experience, some conclusions are made about the effect of changes in the eigenvalues of the Jacobian matrix on the estimated domain of attraction;It is shown how sometimes the concepts of the comparison principle and of stability preserving maps can be combined with the above results and the results due to Brayton and Tong for an efficient analysis of high dimensional systems. In doing so, some new results are established which relate the domain of attraction of the original system to the domain of attraction of a lower dimensional comparison system and which rephrases the comparison principle in terms of stability preserving maps.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Narotham Reddy Sarabudla
Sarabudla, Narotham Reddy, "Stability analysis of complex dynamical systems: some computational methods " (1981). Retrospective Theses and Dissertations. 6944.