Multivariable Sectors and Nonlinear Stability. Part 2: A Generalization of the Circle Criterion

摘要

The use of appropriate sector conditions in conjuction with the decomposition of a linear operator into two linear operators, phi and G-phi, where phi has a normal transfer function matrix, leads to a useful stability criterion for a class of multivariable nonlinear feedback systems. This sector approach is adopted and the decomposition of the linear operator is used order to define frequency dependent sectors, which leads to a natural extension of the circle criterion to the multivariable case. The result has a simple graphical interpretation and lends itself to a computer implementation which can be shown to be numerically stable.