On the link between storage functions of allpass systems and Gramians

In this paper, we bring out a link between storage functions of allpass systems and observability/controllability Gramians. We show that under a particular transformation, the storage function of an allpass system is induced by an identity matrix. Interestingly, certain algebraic relations between the states and costates/dual states of an allpass system capture the information of the storage function of the system. Further, we also prove that certain difference dynamics between states and costates of an allpass system is always present in the orthogonal complement of its controllable subspace.

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