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Mathematical Problems in Engineering
Volume 2012, Article ID 721382, 10 pages
http://dx.doi.org/10.1155/2012/721382
Research Article

Lyapunov Stability of Quasiperiodic Systems

Department of Engineering Technology, Arizona State University, Mesa, AZ 85212, USA

Received 31 December 2011; Revised 18 February 2012; Accepted 23 February 2012

Academic Editor: Oleg V. Gendelman

Copyright © 2012 Sangram Redkar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present some observations on the stability and reducibility of quasiperiodic systems. In a quasiperiodic system, the periodicity of parametric excitation is incommensurate with the periodicity of certain terms multiplying the state vector. We present a Lyapunov-type approach and the Lyapunov-Floquet (L-F) transformation to derive the stability conditions. This approach can be utilized to investigate the robustness, stability margin, and design controller for the system.