Bicoprime factor stability criteria for linear time-varying systems in the nest algebra

ABSTRACT

This paper presents a bicoprime factorisation approach to deal with various stability problems for linear discrete time-varying systems within the framework of nest algebra. First, we show that a system has a bicoprime factorisation if and only if it has a right and left coprime factorisation by using the complete finiteness of the nest algebra. Based on the bicoprime factorisations, some stability criteria for internal stability and strong stabilisability are obtained, which generalises similar results for linear time-invariant systems. Finally, we derive a necessary and sufficient condition for simultaneous stabilisability of two systems, Additionally, the condition given in this paper lead to a constructive controller design to stabilise simultaneously two systems.

Keywords:

• Bicoprime factorisations
• linear time-varying systems
• stability
• nest algebra

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [No. 11501182].