5 papers
A Globally Asymptotically Stable Planar Homogeneous Polynomial Vector Field With No Polynomial Lyapunov Function
Jun Liu, Maxwell Fitzsimmons
We disprove the conjecture that every globally asymptotically stable homogeneous polynomial vector field admits a homogeneous polynomial Lyapunov function. The counterexample is a…
A Converse Control Lyapunov Theorem for Joint Safety and Stability
Thanin Quartz, Maxwell Fitzsimmons, Jun Liu
We show that the existence of a strictly compatible pair of control Lyapunov and control barrier functions is equivalent to the existence of a single smooth Lyapunov function that…
Formal Verification of Control Lyapunov-Barrier Functions for Safe Stabilization with Bounded Controls
Jun Liu
We present verifiable conditions for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety under bounded controls. These sufficient con…
Computing Control Lyapunov-Barrier Functions: Softmax Relaxation and Smooth Patching with Formal Guarantees
Jun Liu, Maxwell Fitzsimmons
We present a computational framework for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety. We show that the existence of a strictl…
Symbolic Reduction for Formal Synthesis of Global Lyapunov Functions
Jun Liu, Maxwell Fitzsimmons
We investigate the formal synthesis of global polynomial Lyapunov functions for polynomial vector fields. We establish that a sign-definite polynomial must satisfy specific algebra…