nonlinear dynamics

A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function

  • Amir Ali Ahmadi
  • Bachir El Khadir
    • Categories Control Applications, Semi-definite Programming, Systems governed by Differential Equations Optimization Tags , , , ,

    We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally. Citation Submitted for publication Article Download View A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function

    SOS-Convex Lyapunov Functions and Stability of Difference Inclusions

  • Amir Ali Ahmadi
  • Raphaël Jungers
    • Categories Control Applications, Convex Optimization, Semi-definite Programming Tags , , , , ,

    We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an algebraic certificate of convexity and that can be efficiently found via semidefinite programming. We prove that sos-convex Lyapunov functions are universal (i.e., necessary … Read more

    On Algebraic Proofs of Stability for Homogeneous Vector Fields

  • Amir Ali Ahmadi
  • Bachir El Khadir
    • Categories Control Applications, Semi-definite Programming, Systems governed by Differential Equations Optimization Tags , , ,

    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 (i.e., a rational function). We further show that when the vector field is polynomial, the Lyapunov inequalities on both the rational function and its derivative have sum of squares … Read more

    Gas Network Optimization: A comparison of Piecewise Linear Models

  • Carlos M. Correa-Posada
  • Pedro Sanchez-Martan
    • Categories (Mixed) Integer Linear Programming, Chemical Engineering Tags , , , , ,

    Gas network optimization manages the gas transport by minimizing operating costs and fulfilling contracts between consumers and suppliers. This is an NP- hard problem governed by non-convex and nonlinear gas transport functions that can be modeled by mixed integer linear programming (MILP) techniques. Under these methods, piecewise linear functions describe nonlinearities and bi- nary variables … Read more