ℓ2-stability: The cases of infinite dimensional discrete autonomous systems and 2-D autonomous systems. (October 2017)

• Record Type: Journal Article
• Authors: Athalye, Chirayu D.; Pal, Debasattam; Pillai, Harish K.
• Is Part Of: Automatica. Volume 84(2017)
• Page Start: 70
• Page End: 78
• Publication Date: 2017-10
• Subjects: Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2017.06.028
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: In this paper, we analyze ℓ 2 -stability of infinite dimensional discrete autonomous systems given in a state space form with state transition matrix being a Laurent polynomial matrix A ( σ, σ − 1 ) in the shift operator σ . We give sufficient conditions and necessary conditions for ℓ 2 -stability of such systems. We then use the theory of ℓ 2 -stability, thus developed, to analyze ℓ 2 -stability of discrete 2-D autonomous systems. We achieve this by showing how a discrete 2-D autonomous system can be converted to an equivalent infinite dimensional state space discrete autonomous system, where the state transition matrix turns out to be a Laurent polynomial matrix in the shift operator. Finally, we provide some easy-to-check numerical tests for ℓ 2 -stability of the above-mentioned type of systems.