Tutorial Guide: Enhanced MATLAB Tools for Linear and Nonlinear System Stability Analysis

Three matlab-based tools have been developed for the convenient assessment of stability conditions for linear and nonlinear systems. The first is a more helpful and definitive version of nyquist, which has features of automatic zooming (to show all crossings of the real axis and thus display the corresponding critical gain points) and which displays on the real axis a numeral (‘0’, ‘1’ etc.) that represents the number of unstable (right-half-plane) poles that would result for a closed-loop system with feedback gain k if −1/k is located in that region. The second tool is built on this extended nyquist command, and makes the application of the nonlinear time-varying system Circle Criterion equally simple and definitive. The third routine implements the Popov criterion for nonlinear time-invariant systems, which typically produces substantially less restrictive sector constraints than the Circle Criterion, as one would expect due to assumption of time invariance. Examples are presented to show the use and efficacy of these extensions within the matlab environment.