Modal Series Coefficients Estimation by LMI-based Approach for Nonlinear Systems Identification

Dynamic systems analysis and achieve closed form time response of these systems has been an attractive field of interest for mathematicians and engineers. Unlike linear dynamic systems there isn´t any general solution for nonlinear ones. This seems to be impossible and nobody can proposed exact solution of obtaining nonlinear systems closed form response. Therefore, for nonlinear systems the only way is using approximate closed form solutions. Modal series is a novel method of obtaining closed form solution of nonlinear systems. Our purpose in this paper is to estimate modal coefficients of zero input response of nonlinear systems with a method without any complexity of analytical algorithms that satisfies our desire accuracy. The purpose is to obtain closed form response for nonlinear systems just from some observations and measurement values. In this research first modal contents of nonlinear system response was identified by Prony analysis then modal series coefficients was evaluated with a new method based on linear matrix inequalities (LMI). Simulation results for a second order nonlinear system is available to verify the effectiveness of our approach