LMI Stability Tests for the Fornasini-Marchesini Model

We present a linear matrix inequality (LMI) for testing the stability of a 2-D system described by the Fornasini-Marchesini first model. The test is based on the properties of sum-of-squares polynomials with matrix coefficients. Although the test implements a sufficient condition, extensive experiments suggest that the gap to necessity is very small. We also derive an LMI describing stability conditions around a given model and useful in robust stability testing.