Linearization of Nonlinear Dynamical Systems: A Comparative Study

Linearization of nonlinear dynamical systems is a main approach in the designing and analyzing of such systems. Optimallinear model is an online linearization technique for finding a local model that is linear in both the state and the control terms.In this paper, a comparison between the performance of both optimal linear model and Jacobian linearization technique isconducted. The performance of these two linearization methods are illustrated using two benchmark nonlinear systems, theseare inverted pendulum system; and Duffing chaos system. These two systems where chosen because they are inherentlynonlinear unstable systems.