Title data
Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2013
.  6 p.
There is a more recent version of this item available. 
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Abstract in another language
We present a novel numerical technique for the computation of a Lyapunov function for nonlinear systems with an asymptotically stable equilibrium point. Our proposed approach constructs a continuous piecewise affine (CPA) function given a suitable partition of the state space, called a triangulation, and values at the vertices of the triangulation. The vertex values are obtained from a Lyapunov function in a classical converse Lyapunov theorem and verification that the obtained CPA function is a Lyapunov function is shown to be equivalent to verification of several simple inequalities. Furthermore, by refining the triangulation, we show that it is always possible to construct a CPA Lyapunov function. Numerical examples are presented demonstrating the effectiveness of the proposed method.
Further data
Item Type:  Preprint, postprint, working paper, discussion paper 

Keywords:  Lyapunov methods; nonlinear control systems; asymptotic stability; linear programming; Yoshizawa construction; statespace methods; approximation methods 
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 07:14 
URI:  https://eref.unibayreuth.de/id/eprint/9469 
Available Versions of this Item
 Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction. (deposited 28 Mar 2015 22:00) [Currently Displayed]