A Globally Asymptotically Stable Polynomial Vector Field with No Polynomial Lyapunov
Function Page 1 A Globally Asymptotically Stable Polynomial Vector Field with no Polynomial …

In this paper, we provide a method to design Lyapunov functions (LFs) for a class of
homogeneous systems described by functions that we call generalized forms (GFs) …

Nonlinear dynamical systems play a crucial role in control systems because, in practice, all
the plants are nonlinear, and they are also a hopeful description of complex robot …

Given a (differentiable) signal, it is an important task for many applications to estimate on
line its derivatives. Some well-known algorithms to solve this problem include the …

In this paper, we develop algorithms for the computational analysis of stability and robust
performance properties of nonlinear models governed by polynomial differential equations …

Learning control has become an appealing alternative to the derivation of control laws
based on classic control theory. However, a major shortcoming of learning control is the lack …

arXiv:1201.2892v1 [math.OC] 13 Jan 2012 Page 1 Algebraic Relaxations and Hardness
Results in Polynomial Optimization and Lyapunov Analysis by Amir Ali Ahmadi BS …

We show that existence of a global polynomial Lyapunov function for a homogeneous
polynomial vector field or a planar polynomial vector field (under a mild condition) implies …

Recent advances in deep learning have bolstered our ability to forecast the evolution of
dynamical systems, but common neural networks do not adhere to physical laws, critical …

We prove that if a homogeneous, continuously differentiable vector field is asymptotically
stable, then it admits a Lyapunov function, which is the ratio of two polynomials (ie, a rational …