Simulation of nonlinear systems by multilinear models via state space linearization



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In general, the study of solutions of nonlinear differential equations requires advanced techniques and some ingenuity. Even today the problems in this area are by no means solved. Particularly, the qualitative investigation of those solutions is even more difficult. There are only a few theorems available for higher order system analysis. This research concentrates on the qualitative analysis; especially the partition of the state space. Two criteria are established: (1) the discriminant criterion which can be applied to the second order nonlinear system, and (2) the generalized Hurwitz Criterion which enables us to partition a high order system in the state space. Because both criteria are based on the Jacobian matrix the presentation starts with that matrix. It is believed that the first criterion is well known and the second criterion is original. This research can be considered as a systematic approach to the nonlinear simulation problem by the use of the multi-linear model technique.