Title data
Björnsson, Jóhann ; Giesl, Peter ; Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2014
.  6 p.
There is a more recent version of this item available. 
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Abstract in another language
The numerical construction of Lyapunov functions provides useful information on system behavior. In the Continuous and Piecewise Affine (CPA) method, linear programming is used to parameterize a CPA Lyapunov function for continuous nonlinear systems. This method is relatively slow due to the linear program that has to be solved. A recent proposal was to parameterize the CPA Lyapunov function based on a Lyapunov function in a converse Lyapunov theorem by Yoshizawa. In this paper we propose parameterizing CPA Lyapunov functions using a Lyapunov function construction in a classic converse Lyapunov theorem by Massera. We provide the theory for such a parameterization and present several examples to illustrate the utility of this approach.
Further data
Item Type:  Preprint, postprint, working paper, discussion paper 

Keywords:  Lyapunov methods; nonlinear control systems; asymptotic stability; linear programming; Massera construction; approximation methods; continuous systems 
Institutions of the University:  Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  28 Mar 2015 22:00 
Last Modified:  30 Mar 2015 07:13 
URI:  https://eref.unibayreuth.de/id/eprint/9470 
Available Versions of this Item
 Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction. (deposited 28 Mar 2015 22:00) [Currently Displayed]