Classical converse theorems in Lyapunov's second method

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October 2015, 20(8): 2333-2360. doi: 10.3934/dcdsb.2015.20.2333

Classical converse theorems in Lyapunov's second method

Christopher M. Kellett ^1,

1.	School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, New South Wales 2308

Received August 2014 Revised March 2015 Published August 2015

Abstract
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Lyapunov's second or direct method is one of the most widely used techniques for investigating stability properties of dynamical systems. This technique makes use of an auxiliary function, called a Lyapunov function, to ascertain stability properties for a specific system without the need to generate system solutions. An important question is the converse or reversability of Lyapunov's second method; i.e., given a specific stability property does there exist an appropriate Lyapunov function? We survey some of the available answers to this question.

Keywords: Lyapunov functions, difference and differential inclusions., stability theory.

Mathematics Subject Classification: Primary: 93D05, 93D30, 93D20; Secondary: 93D1.

Citation: Christopher M. Kellett. Classical converse theorems in Lyapunov's second method. Discrete and Continuous Dynamical Systems - B, 2015, 20 (8) : 2333-2360. doi: 10.3934/dcdsb.2015.20.2333

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