Transfer function conditions for stabilizability

Author

Bhattacharyya, S.P. ; Howze, J.W.

Author_Institution

Texas A & M University, College Station, TX, USA

Volume

Issue

fYear

1984

fDate

3/1/1984 12:00:00 AM

Firstpage

253

Lastpage

254

Abstract

For the linear time invariant system $\\bigl [\\matrix {y_{c}(s)\\cr y_{m}(s)}\\bigr ] = \\bigl [\\matrix{G(s)&H(s)\\cr M(s)&N(s)} \\bigr ] \\bigl [\\matrix {u_{c}(s)\\cr u_{r}(s)}\\bigr ]$ a necessary and sufficient condition based on the proper rational transfer function matrices ${G, H, M, N}$ is given for the existence of a proper stabilizing controller $u_{c}(s) = C(s)y_{m}(s)$ . The condition states that the McMillan degrees of $M^{+}(s)$ and $\\bigl [\\matrix{G^{+}(s)&H^{+}(s)\\cr M{+}(s)&N{+}(s)}\\bigr ]$ must be equal, where ${G^{+}(s), H^{+}(s), M^{+}(s), N^{+}(s)}$ represents the unstable components of the partial fraction expansions of ${G(s), H(s), M(s), N(s)}$ .

Keywords

Stability, linear systems; Transfer function matrices; Control systems; Eigenvalues and eigenfunctions; Matrices; Matrix decomposition; Polynomials; Random access memory; Stability criteria; Testing; Time invariant systems; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1984.1103496

Filename

1103496

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=844478