Certification of Linear Inclusions for Nonlinear Systems

In this letter, we propose a novel method to certify whether a given set of vertex linear systems constitutes a linear difference inclusion for a nonlinear system. The method relies on formulating the verification of the inclusion as an optimization problem in a novel way. The sign of the optimal value of the proposed optimization problem determines whether the candidate set of vertices is a linear difference inclusion for the nonlinear dynamics or not. The result is a Yes/No certificate. Our method can be useful for reducing the conservatism of linear difference inclusions obtained by other conservative methods, or for providing a rigorous certification procedure for any possibly non-rigorous method that aims at finding a linear difference inclusion for a nonlinear system. We illustrate how the method can be useful in obtaining less conservative linear enclosures for nonlinear systems by using small numerical examples. We further demonstrate the applicability of our method to larger systems using an industry-relevant chemical reactor example.