New results on stable multidimensional polynomials. III. State-space interpretations

Author

Basu, Sankar

Author_Institution

Dept. of Electr. Eng., Stevens Inst. of Technol., Hoboken, NJ, USA

Volume

38

Issue

7

fYear

1991

fDate

7/1/1991 12:00:00 AM

Firstpage

755

Lastpage

768

Abstract

Lyapunov characterization of scattering Schur, reactance Schur, and immittance Schur properties of multidimensional polynomials are given. Since these polynomials arise in the description of passive systems, energy-like functions can be conveniently defined for such systems, thus making Lyapunov-type characterization readily available. It is shown that the notion of modal observability and its further variants for multidimensional systems are necessary ingredients of such considerations. Two approaches are followed. One is essentially passive synthesis based, whereas the other is that of viewing multidimensional systems as a parametric family of one-dimensional systems. A nontrivial example is included to illustrate the former method

Keywords

Lyapunov methods; multidimensional systems; polynomials; stability; state-space methods; Lyapunov characterization; energy-like functions; immittance Schur properties; modal observability; multidimensional systems; one-dimensional systems; passive systems; reactance Schur properties; scattering Schur properties; stable multidimensional polynomials; Equations; Lyapunov method; Multidimensional systems; Observability; Polynomials; Scattering; Stability; Symmetric matrices; Transfer functions; Veins;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/31.135747

Filename

135747