Learn Algebraic Systems Theory and Control Design with State Space And Multivariable Theory Rosenbro

Doubly-indexed dynamical systems provide a state space realization of two-dimensional filters which includes previous state models. Algebraic criteria for testing structural properties (reachability, observability, internal stability) are introduced.

This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description (PMD). For a controllable first-order linear state-space system model, by using the right coprime factorization of its transfer function matrix, under the condition that the denominator matrix in the right coprime factorization is column reduced, it is equivalently transformed into a fully actuated PMD model, whose time-domain expression is just a high-order fully actuated (HOFA) system model. This method is a supplement to the previous one in the time-domain, and reveals a connection between the controllability of the first-order linear state-space system model and the full-actuation of its PMD model. Both continuous-time and discrete-time linear systems are considered. Some numerical examples are worked out to illustrate the effectiveness of the proposed approaches.

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