Estimating Domain Of Attraction Based On Bilinear Matrix Inequalities And Sum Of Squares Optimization

The domain of attraction (DOA) of a system is a local asymptotic stable domain. We always hope to obtain the biggest DOA of the system. In many engineering fields, especially those dynamical systems, it is necessary to master the DOA of a system to ensure the system’s safety. So far, there are many methods of estimating the DOA of a system, more over, lots of scholars also open up many new methods of estimating the DOA. But it is very difficult for us to get the exact DOA of a system. In this paper we obtain bigger DOA of the system based on the original method.This paper studies estimating the DOA of nonlinear autonomous systems, we discuss two methods, that is, based on the sum of squares (SOS) optimization algorithm and based on the bilinear matrix inequalities (BMI) optimization algorithm. We separately use these two methods to study two types of systems, which are the two-dimension systems and the three-dimension systems. For the above two methods we analyze the results from their accuracy and running time, the facts indicate that the method based on the BMI optimization is better than the method based on the SOS optimization both in accuracy and running time.When we study the three-dimension system, we study a class SIR infection model with a type of the total population with constant input, we obtain bigger DOA compared with the original method, thus, we reduce the probability of more people infecting the SIR in theory. It has greater practical significance.