Project period: 10/2010 - 10/2014
Project: Stability analysis via coupled Hamilton-Jacobi equations
Co-operation partner: Prof. Dr. Lars Grüne, Uni Bayreuth
Sponsorship: EU
Thematic area: partial differential equations, non-autonomous systems, networked systems

The robust domain of attraction of a fixed point can be computed by solving a particular Hamilton-Jacobi equation which derives from Zubov's method. In practice this approach has a prohbitive cost already for systems of moderate dimensions because solutions require the gridding of the state space of the dynamical systems. Even adaptive gridding techniques do not provide sufficient savings in order to push the boundaries of applicability beyond dimensions fice or six.
Frequently, systems of higher dimension are already given as the interconnection of several lower-dimensional systems. In the project we utilize this additional structure to develop methods which only rely on numerical computations for the lower-dimensional subsystems. Properties of the interconnected system will then be concluded from nonlinear small-gain theorems.
The necessary computation of robust Lyapunov functions for the lower-dimensional systems will be pursued in the Hamilton-Jacobi framework and also using linear programming techniques for the explicit numerical construction of Lyapunov functions.