Decompositions of Proper Systems
We present in this chapter the structural decomposition of linear time-invariant systems as represented by a matrix triple or a matrix quadruple. In order to make the presentation easier to follow, we will start with the structural decomposition of single-input and single-output (SISO) systems. It will be followed by a detailed construction of the structural decomposition for a general strictly proper multi-input and multi-output (MIMO) system. The decomposition of a general nonstrictly proper MIMO system will then be given together with detailed proofs of system properties revealed under the decomposition. We will conclude the chapter with the structural decomposition of general discrete-time systems.
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