Browsing by Author "Hagan, Martin"

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    Forward and Converse Lyapunov Theorems for Discrete Dynamical Systems
    Jafari, Reza; Kable, Anthony; Hagan, Martin (IEEE, 2014-08-20)
    This paper derives the necessary and sufficient conditions for the Lyapunov function such that the equilibrium point of a dynamical system is stable or Globally Asymptotic Stable (GAS). The paper shows that continuity of Lyapunov function at the equilibrium point is the only necessary and sufficient condition for stability. We shows that a certain type of converse theorem can not be proved with continuous Lyapunov function. The Tower of Babel ‘TOB’ is given as an example of stable dynamical system in which no continuous Lyapunov function exists for this system.
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    Global stability analysis using the method of Reduction Of Dissipativity Domain
    Jafari, Reza; Hagan, Martin (IEEE, 2011-07)
    This paper describes a modification to the method of Reduction Of Dissipativity Domain with Linear Boundaries (RODD-LB1) which was introduced by Barabanov and Prokharov [7]. The RODD method is a computational technique for the global stability analysis of nonlinear dynamic systems. In this paper we introduce an extension to the original RODD method that is designed to speed up convergence. The efficiency of the extended algorithm is demonstrated through numerical examples.