The Stability Analysis of Linear Multivariable Systems with Antisymmetric Cross-Connections

Abstract

The stability of linear multivariable systems, consisting of identical channels and having antisymmetric cross-connections, is examined.
By considering that the structural features of multivariable systems have been classified into P, V and H-canonical structures, the transfer functions with complex coefficients are derived for each structure, and they are termed as the complex transfer function.
Further, it is shown that n-channel systems under consideration are described from the view point of stability in the form of series connection of the subsystems made up of one or two-channels.
In a composite system, consisting of two-channel systems, the stability of the entire system can be investigated by analyzing the stability of the individual subsystems.
It is also shown that the entire system can be extensively stabilized by attaching a two-channel system with antisymmetric cross-connection to any dynamic system.