MATLAB Tools for Linear and Nonlinear System Stability Theorem Implementation

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 will occur in a closed-loop system with feedback gain k if the point −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. Finally, a Popov Criterion tool is included to achieve better sector bounds for the nonlinear timeinvariant case. Examples are presented to show the efficacy of these extensions within the matlab environment.