Multivariable Sectors and Nonlinear Stability. Part 1: The Use of Sectors in the Derivation of Stability Criteria for Nonlinear Multivariable Systems

摘要

The definition and properties of the sector of scalar systems are extended to systems with many-inputs and many-outputs. On the basis of these definitions it is possible to state a simple stability criterion for a class of nonlinear multivariable systems. A suitable decomposition of the linear element G of the nonlinear feedback system, enables the derivation of a generalization of the circle criterion. This involves the frequency response of the eigenvalues of a normal matrix and an expanded version of the classical on-axis circle. The expansion of the circle is due to the deviation of the transfer function matrix of G from normality which is measured by appropriate sector conditions o the error operator G-phi.