Checking Structural Stability of BDC-Decomposable Systems via Convex Optimisation
Franco Bianchini (Università degli Studi di Udine)
Graziano Chesi (The University of Hong Kong)
Patrizio Colaneri (Politecnico di Milano)
G. Giordano (TU Delft - Team Tamas Keviczky)
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Abstract
In this letter we show how the problem of assessing structural local stability of BDC-decomposable systems, left open in recent literature, can be solved via convex optimisation. First we give a simple test, based on a sufficient condition, that requires checking the strict co-positivity of a multivariate polynomial. Then we provide a stronger test, based on a necessary and sufficient condition, which can be numerically implemented via LMI-based convex optimisation. The proposed approach certifies the structural stability of non-trivial systems, including a biological network discussed in the literature.