123 citations · 525 across the 31 of their papers we have counts for
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math.OC2011
On the Difficulty of Deciding Asymptotic Stability of Cubic Homogeneous Vector Fields
Amir Ali Ahmadi
It is well-known that asymptotic stability (AS) of homogeneous polynomial vector fields of degree one (i.e., linear systems) can be decided in polynomial time e.g. by searching for…
math.OC2011★ 64 cited
A Complete Characterization of the Gap between Convexity and SOS-Convexity
Amir Ali Ahmadi, Pablo A. Parrilo
Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials, via the definition of convexity,…
math.OC2011★ 120 cited
Joint Spectral Radius and Path-Complete Graph Lyapunov Functions
Amir Ali Ahmadi, Raphaël Jungers, Pablo A. Parrilo +1
We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switche…