ANALYSIS OF LYAPUNOV STABILITY THEORY FOR DYNAMICAL SYSTEMS. MATHCAD VERIFICATION ALGORITHMS

Dan Mihai MIRONESCU

Abstract


This article contains a synthesis of the basic concepts from the Lyapunov’s stability theory defining the notions of equilibrium, uniform stability, asymptotic stability, globally exponential stability and Lyapunov functions. Lyapunov’s direct method is discussed, complete with an analysis of the evolution of a dynamical system in the phase plane conducted with the aid of Mathcad software.
For dynamical autonomous systems the LaSalle theorem is used in the analysis of stability of motion, complementary to Lyapunov’s direct method.
Keywords: Lyapunov stability; Mathcad Programme; stability analysis of manipulators and robot motion.


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