The general problem of stability of motion en ingles primera edicion. Most proofs of lyapunovs theorem i know are highly nonconstructive. Lyapunov criteria for uniform convergence of conditional. Distributed under a creative commons attribution 4. Rothblum, a proof of the convexity of the range of a nonatomic vector measure using linear inequalities, linear algebra and its applications, volume 199, supplement 1, 1 march 1994, pages 373379.
On characterizations of the inputtostate stability pro perty. Nov, 2018 defining stability using lyapunov functions energy functions duration. Estabilidad por lyapunov sistemas dinamicos lineales. Based on your location, we recommend that you select. The method is a generalization of the idea that if there is some measure of energy in a system, then. We denote by the stable set and by the unstable set of the theorem states that is a smooth manifold and its tangent space has the same dimension as the stable space of the linearization of at.
Files are available under licenses specified on their description page. All structured data from the file and property namespaces is available under the creative commons cc0 license. Unidad 3 estabilidad 1 by pedro daniel lara maldonado. Outline autonomous systemsinvariance principlelinear system and linearization lyapunov and lasalle appl. For a relatively constructive proof, see alan hoffman, uriel g. Lyapunov s direct method also called the second method of lyapunov allows us to determine the stability of a system without explicitly integrating the di. Lyapunov functionals and stability of stochastic difference equations is primarily addressed to experts in stability theory but will also be of use in the work of pure and computational mathematicians and researchers using the ideas of optimal control to study economic, mechanical and biological systems.
Choose a web site to get translated content where available and see local events and offers. Lyapunov equations arise in several areas of control, including stability theory and the study of the rms behavior of systems. Lyapunov was a pioneer in successful endeavoring to develop the global approach to the analysis of the stability of nonlinear dynamical systems by. Pdf lyapunov based stability analysis for metro lines.
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