Sylvie Putot - Academia.edu (original) (raw)

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Papers by Sylvie Putot

Proc. of the Int. Space …, 2009

2000 International Conference on Simulation Semiconductor Processes and Devices (Cat. No.00TH8502), 2000

1999 International Conference on Simulation of Semiconductor Processes and Devices. SISPAD'99 (IEEE Cat. No.99TH8387), 1999

Lecture Notes in Computer Science, 2002

Lecture Notes in Computer Science, 2005

Lecture Notes in Computer Science, 2009

International Electron Devices Meeting 1999. Technical Digest (Cat. No.99CH36318), 1999

Lecture Notes in Computer Science, 2004

2014 American Control Conference, 2014

ABSTRACT In this paper, we focus on finding positive invariants and Lyapunov functions to establi... more ABSTRACT In this paper, we focus on finding positive invariants and Lyapunov functions to establish reachability and stability properties, respectively, of polynomial ordinary differential equations (ODEs). In general, the search for such functions is a hard problem. As a result, numerous techniques have been developed to search for polynomial differential variants that yield positive invariants and polynomial Lyapunov functions that prove stability, for systems defined by polynomial differential equations. However, the systematic search for non-polynomial functions is considered a much harder problem, and has received much less attention. In this paper, we combine ideas from computer algebra with the Sum-Of-Squares (SOS) relaxation for polynomial positive semi-definiteness to find non polynomial differential variants and Lyapunov functions for polynomial ODEs. Using the well-known concept of Darboux polynomials, we show how Darboux polynomials can, in many instances, naturally lead to specific forms of Lyapunov functions that involve rational function, logarithmic and exponential terms.We demonstrate the value of our approach by deriving non-polynomial Lyapunov functions for numerical examples drawn from the literature.