Algebraic Theory of Two-Channel Decentralized Control Systems

A two-channel multiinput-multioutput linear time-invariant decentralized control system is analyzed in a general algebraic framework. Necessary and sufficient conditions for decentralized stabilizability are obtained in an algebraic setting and interpreted in terms of fixed-eigenvalues in the case of rational transfer functions. The class of all decentralized stabilizing compensators is given; this class is parametrized by two parameter matrices, which are not completely free. The results apply to distributed or lumped, discrete-time or continuous-time systems.