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A survey of linear singular systems. (English) Zbl 0613.93029

This is a historical survey of system theory for singular linear systems, i.e., systems of the form Eẋ\(=Ax+Bu\) with E possibly singular. Topics discussed include: a formula for the solution (extending the variation of constants formula), controllability and observability, stability and feedback, regulator theory, classification and equivalence.
Reviewer: P.Brunovsky

MSC:

93C05 Linear systems in control theory
15A09 Theory of matrix inversion and generalized inverses
34A99 General theory for ordinary differential equations
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
49J15 Existence theories for optimal control problems involving ordinary differential equations
49K15 Optimality conditions for problems involving ordinary differential equations
93B05 Controllability
93B07 Observability
93D15 Stabilization of systems by feedback
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