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A tutorial on the geometric analysis of linear time-invariant implicit systems. (English) Zbl 0745.93033
Summary: A background of recent work in nonregular and regular implicit systems of the form \(E\dot x=Ax+Bu\) is provided. Then, the output-nulling, unknown- input and composite subspaces are defined for singular systems, with recursion given for their computation. Inner subspaces, that is those in the domain of \(E\) and \(A\), are distinguished from outer subspaces, those in the codomain of \(E\) and \(A\). The notions of composite preimage and composite image are introduced. The result is a framework that unifies some of the recent work in the geometric theory of implicit systems. System properties are discussed for both regular and nonregular systems, and duality is investigated.

MSC:
93C15 Control/observation systems governed by ordinary differential equations
93B27 Geometric methods
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