On the existence of complex roots of real polynomials

Abstract

This paper is concerned with the existence problem of complex roots of real polynomials with degree , which is derived from the study of near-controllability of a class of discrete-time bilinear systems. Some sufficient conditions for the existence of complex roots are presented, which are easy to apply.

Keywords:

• complex roots
• real polynomials
• commutative matrices
• discrete-time bilinear systems
• near-controllability

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the China Postdoctoral Science Foundation funded project [grant number 2012T50035]; National Natural Science Foundation of China [grant number 61203231].