Structural Completeness of a Multi-channel Linear System with Dependent Parameters
This work addresses the problem of decentralized control for multi-channel linear systems, offering theoretical conditions to ensure structural completeness, which is important for system stabilization.
The paper provides necessary and sufficient algebraic conditions for a multi-channel linear system with dependent parameters to be structurally complete (i.e., have no fixed spectrum for almost all parameter values), and also gives an equivalent graphical condition for a certain parameterization type.
It is well known that the "fixed spectrum" {i.e., the set of fixed modes} of a multi-channel linear system plays a central role in the stabilization of such a system with decentralized control. A parameterized multi-channel linear system is said to be "structurally complete" if it has no fixed spectrum for almost all parameter values. Necessary and sufficient algebraic conditions are presented for a multi-channel linear system with dependent parameters to be structurally complete. An equivalent graphical condition is also given for a certain type of parameterization.