A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function
Copyright policy )A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function
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.
Fixed minor typos. To appear in Systems & Control Letters
- Princeton University
- Google (United States) United States
- Princeton University
- College of New Jersey United States
- Princeton University
Asymptotic stability in control theory, polynomial Lyapunov functions, Systems and Control (eess.SY), Dynamical Systems (math.DS), Electrical Engineering and Systems Science - Systems and Control, nonlinear dynamics, polynomial vector fields, algorithms for testing asymptotic stability, Optimization and Control (math.OC), Lyapunov and storage functions, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Nonlinear systems in control theory, sum of squares optimization, Mathematics - Dynamical Systems, Mathematics - Optimization and Control, Control/observation systems governed by ordinary differential equations
Asymptotic stability in control theory, polynomial Lyapunov functions, Systems and Control (eess.SY), Dynamical Systems (math.DS), Electrical Engineering and Systems Science - Systems and Control, nonlinear dynamics, polynomial vector fields, algorithms for testing asymptotic stability, Optimization and Control (math.OC), Lyapunov and storage functions, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Nonlinear systems in control theory, sum of squares optimization, Mathematics - Dynamical Systems, Mathematics - Optimization and Control, Control/observation systems governed by ordinary differential equations
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