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Generalized reachability subspaces for singular systems. (English) Zbl 0689.93004
The concept of reachability subspace is extended to generalized state space systems described by differential equations of the form $$E\dot x=Ax+Bu$$, $$\det(sE-A)\not\equiv 0$$. A subspace R is defined to be a generalized reachability subspace (respectively, controllability subspace) of such a system if there exists a feedback matrix F and an input transformation matrix G such that R is the reachable (resp. controllable) subspace of the system $$E\dot x=(A+BF)x+BGv$$ satisfying $$\det (sE-(A+BF)\not\equiv 0$$. It is shown that R is a generalized reachability subspace if and only if it is an (E,A,B)-invariant almost reachability subspace. A corresponding characterization of generalized controllability spaces is also given. Finally, spectral assignability properties of generalized reachability and controllability spaces are discussed.
Reviewer: D.Hinrichsen

MSC:
 93B05 Controllability 34A99 General theory for ordinary differential equations 93B27 Geometric methods 93C05 Linear systems in control theory 93C35 Multivariable systems, multidimensional control systems
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