Formal Verification of Stability for Parametric affine Switched Systems

We focus on switched systems with a parametric affine term and state-dependent switch logic. For these systems, we aim to synthesize a region of parameters for which we guarantee a formal proof of Global Asymptotic Stability (GAS). We propose a novel technique based on Piecewise Quadratic Lyapunov Functions that are either Locally Valid (LVPQLF) or Parametric (PPQLF), for which we can define the LMI problem for synthesis and the symbolic proof obligations for formal verification. We implement the technique and show that it scales up to industrial-size systems with 21 state variables.