Stability of fractional-order linear time-invariant systems with multiple noncommensurate orders

Authors:
Zhuang Jiao;Yang Quan Chen
Affiliations:
Department of Automation, Tsinghua University, Beijing, 100084, PR China and Center for Self-Organizing and Intelligent Systems(CSOIS), Electrical and Computer Engineering Department, Utah State U ...;Center for Self-Organizing and Intelligent Systems(CSOIS), Electrical and Computer Engineering Department, Utah State University, Logan, UT 84322, USA
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

Bounded-input bounded-output stability conditions for fractional-order linear time-invariant (LTI) systems with multiple noncommensurate orders have been established in this paper. The orders become noncommensurate orders when they do not have a common divisor. Sufficient and necessary conditions of stability for a fractional-order LTI system with multiple noncommensurate orders are presented in two cases. Based on the numerical inverse Laplace transform technique, time-domain responses for a fractional-order system with double noncommensurate orders are presented to illustrate the obtained stability results.