Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach

• Published in: IEEE transactions on automatic control Vol. 54; no. 6; pp. 1294 - 1299
• Main Authors: LU, Jun-Guo, GUANRONG CHEN
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Automatic control; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Costs; Dynamic programming; Exact sciences and technology; Fractional-order system; Integral equations; interval system; Intervals; Linear matrix inequalities; linear matrix inequality (LMI); Optimal control; Quantization; Robust stability; robust stabilization; Stability; Stabilization; Robust stability; robust stabilization; Necessary and sufficient condition; Stabilization; Control synthesis; interval system; linear matrix inequality (LMI); Fractional derivative; Robust control; Linear matrix inequality; Interval matrix; Robustness; Fractional-order system
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2009.2013056

This technical note presents necessary and sufficient conditions for the stability and stabilization of fractional-order interval systems. The results are obtained in terms of linear matrix inequalities. Two illustrative examples are given to show that our results are effective and less conservative for checking the robust stability and designing the stabilizing controller for fractional-order interval systems.