Stability of quaternionic linear systems

Author

Pereira, Ricardo ; Vettori, Paolo

Author_Institution

Dept. de Matematica, Univ. de Aveiro, Portugal

Volume

51

Issue

3

fYear

2006

fDate

3/1/2006 12:00:00 AM

Firstpage

518

Lastpage

523

Abstract

The main goal of this paper is to characterize stability and bounded-input-bounded-output (BIBO)-stability of quaternionic dynamical systems. After defining the quaternion skew-field, algebraic properties of quaternionic polynomials such as divisibility and coprimeness are investigated. Having established these results, the Smith and the Smith-McMillan forms of quaternionic matrices are introduced and studied. Finally, all the tools that were developed are used to analyze stability of quaternionic linear systems in a behavioral framework.

Keywords

input-output stability; linear systems; matrix algebra; polynomials; time-varying systems; Smith quaternionic matrix; Smith-McMillan quaternionic matrix; bounded-input-bounded-output stability; quaternion skew-field; quaternionic dynamical systems; quaternionic linear systems stability; quaternionic polynomials; Automatic control; Communication system control; Control systems; Delay; Filtering; Linear systems; Nonlinear systems; Robust control; Stability; Stochastic systems; Behaviors; quaternions; stability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2005.864202

Filename

1605415