期刊
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
卷 16, 期 1, 页码 142-157出版社
SPRINGERNATURE
DOI: 10.2478/s13540-013-0010-2
关键词
fractional-order system; convex polytopic uncertainty; robust stability; robust stabilization; linear matrix inequality (LMI)
资金
- National Natural Science Foundation of China [60974002, 60934006, 61175088]
This paper considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems with convex polytopic uncertainties. The stability condition of the fractional-order linear time-invariant systems without uncertainties is extended by introducing a new matrix variable. The new extended stability condition is linear with respect to the new matrix variable and exhibits a kind of decoupling between the positive definite matrix and the system matrix. Based on the new extended stability condition, sufficient conditions for the above robust stability and stabilization problems are established in terms of linear matrix inequalities by using parameter-dependent positive definite matrices. Finally, numerical examples are provided to illustrate the proposed results.
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