Computational and Applied Math Proseminar

Monday, Otober 22, 1:30 p.m. PSA 206

Sergey Dashkovskiy

Dept. Math. & Stats

On Stability Properties of Networks of Nonlinear Systems

Abstract We will consider a number of nonlinear systems which are interconnected in a network. Stability of nonlinear systems can be described in terms of input-to-state stability (ISS). After a short introduction of this notion we will consider a network of systems where each system is assumed to be ISS. In general such an interconnection is not ISS. We are looking for stability conditions for such networks.

In case of feedback interconnections of two ISS systems such condition of a small-gain type were derived in 1994. A construction of an ISS-Lyapunov function for this case was performed in 1996. In my presentation I will show a stability condition for a general interconnection of many systems and a construction of an ISS-Lyapunov function for a network. As we will see our condition is a natural generalization of the results mentioned above. We will consider some interpretations of this generalized small-gain condition and discuss on approaches how to check this condition numerically.

For further information please contact: mittelmann@asu.edu