Input–Output Finite-Time Stability of Fractional-Order Positive Switched Systems
- 126 Downloads
Input–output finite-time stability (IO-FTS) of fractional-order positive switched systems (FOPSS) is investigated in this paper. First of all, the concept of IO-FTS is extended to FOPSS. Then, by using co-positive Lyapunov functional method together with average dwell time approach, some sufficient conditions of input–output finite-time stability for the considered system are derived. Furthermore, the state feedback controller and the static output feedback controller are designed, and sufficient conditions are presented to ensure that the corresponding closed-loop system is input–output finite-time stable. These conditions can be easily obtained by linear programming. Finally, three numerical examples are given to show the effectiveness of the theoretical results.
KeywordsFractional-order systems Positive switched systems Input–output finite-time stability
This work was supported by the National Natural Science Foundation of China under Grant 61403241 and the Fundamental Research Funds for the Central Universities under Grant GK201703009.
- 7.R. Hilfer, Applications of fractional calculus in physics (World Scientific, Hackensack, 2001), pp. 1–131Google Scholar
- 10.S.P. Huang, H.R. Karimi, Z.P. Xiang, Input-output finite-time stability of positive switched linear systems with state delays, in 2013 9th Asian Control Conference (ASCC), pp. 1–6 (2013)Google Scholar
- 12.T. Kaczorek, Selected problems of fractional systems theory (Springer, Berlin, 2012), pp. 48–54Google Scholar
- 19.W. Malesza, Positive fractional variable order discrete-time systems. Int. Fed. Autom. Control (IFAC) 50(1), 8072–8076 (2017)Google Scholar
- 24.D. Peter, Short time stability in linear time-varying systems. in Proceeding of the IRE International Convention Record Part 4, pp. 83–87 (2014)Google Scholar
- 32.X.D. Zhao, State-dependent switching control of switched positive fractional order systems. ISAT 62, 103–108 (2016)Google Scholar