×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI