Frequency-Domain Criteria for Controllability and Observability of Multivariable Systems

The paper investigates the controllability and observability of multivariable systems in the frequency-domain. A criterion involving pole-zero cancellations determines controllability and observability of multivariable systems. The results are extended to composite systems where necessary and sufficient conditions for the controllability and observability of tandom, feedback and parallel connections of two systems are obtained in terms of the pole and zero polynomials of individual systems. The connection between controllability/ observability and fixed modes in decentralized systems is also discussed.