Stability analysis of non-linear multivariable systems

Abstract

Two dimensional non-linear multivariable systems with single valued non-linearities are analysed for stability, by replacing the non-linearities by their describing functions N1 and N2 . Symmetric systems can be analysed easily as the characteristic equation can be factoriozed and the Nyquist criterion helps to find the existence of the limit cycle in the system. In the antisymmetric case, the characteristic equation is partitioned into real and imaginary parts and these are solved for N1 , and N2 and are plotted in the N1 versus N2 plane. The existence of the limit cycle is indicated by intersection of certain curves (at the same frequency) in the N1 -N1 plane. The stability of the limit cycle is determined by the perturbation technique.