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Author Pettersson, Stefan ♦ Lennartson, Bengt
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Exponential Stability ♦ Converse Theorem ♦ Piecewise Quadratic Lyapunov Function ♦ Necessary Condition ♦ Scalar Auxiliary Function ♦ Introduction Stability ♦ Stable System ♦ Stability Problem ♦ Autonomous Nonlinear System ♦ Dynamical System ♦ Autonomous Nonlinear Dynamical System ♦ Lyapunov Stability ♦ Global Piecewise Quadratic Lyapunov Function ♦ Discontinuous Lyapunov Function ♦ Russian Mathematician ♦ Different Kind ♦ Equilibrium Point ♦ Central Property ♦ Engineer A.m. Lyapunov
Abstract We present sufficient and necessary conditions for exponential stability of autonomous nonlinear dynamical systems using piecewise quadratic Lyapunov functions. The necessary conditions are given as a converse theorem guaranteeing the existence of a global piecewise quadratic Lyapunov function for an exponentially stable system. Keywords: Stability, Exponential Stability, Lyapunov Stability, Discontinuous Lyapunov functions, Piecewise quadratic Lyapunov functions, Converse theorem. 1 Introduction Stability is one of the central properties in systems theory and engineering. Different kind of stability problems arise in the study of dynamical systems. This paper focuses on exponential stability of equilibrium points of autonomous nonlinear systems. Commonly, stability is shown by the theory introduced by the Russian mathematician and engineer A.M. Lyapunov, and the theory now carries his name. Stability can be shown by verifying the existence of a scalar auxiliary function satisfying ce...
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article