An Algorithm for Testing Global Stability of 1D Quadratic PDEs using Semidefinite Programming

The purpose of this code is to test global stability of scalar, 1D, quadratic PDEs, by testing for existence of a quadratic Lyapunov function. The code includes a few examples, namely Burgers' Equation, Kortweg-De Vries Equation, and Kuramoto-Sivashinsky Equation, for which stability can be tested by setting "use_example" in line 27 of "Test_Stability_Quadratic_PDE" equal to 1, 2, or 3, respectively. Alternatively, users can declare their own quadratic PDE within the script "Test_Stability_Quadratic_PDE", specifying the linearized system using the interface provided by PIETOOLS, and declaring the quadratic terms by specifying the coefficients and orders of the derivatives of the state associated to each term. See the comments in the script for more information. For theoretical background regarding the codes, we refer to arXiv:2303.16448.