Input–Output Finite-Time Stability of Fractional-Order Positive Switched Systems

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.

[1]  Hamid Reza Karimi,et al.  Input-output finite-time stability of positive switched linear systems with state delays , 2013, 2013 9th Asian Control Conference (ASCC).

[2]  Hamid Reza Karimi,et al.  Input-Output Finite-Time Stability of Discrete-Time Impulsive Switched Linear Systems with State Delays , 2014, Circuits Syst. Signal Process..

[3]  Yong Zhou,et al.  LMI-based robust control of fractional-order uncertain linear systems , 2011, Comput. Math. Appl..

[4]  Inés Tejado,et al.  Stability of fractional order switching systems , 2012, Comput. Math. Appl..

[5]  V. Lakshmikantham,et al.  Basic theory of fractional differential equations , 2008 .

[6]  Yun Chen,et al.  Finite-Time Stability and Stabilization of Fractional Order Positive Switched Systems , 2016, Circuits, Systems, and Signal Processing.

[7]  Leipo Liu,et al.  Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays , 2017, J. Control. Sci. Eng..

[8]  Luyao Wang,et al.  A Refinement of Gronwall-Bellman Inequality , 2016 .

[9]  Mohammed Chadli,et al.  New admissibility conditions for singular linear continuous-time fractional-order systems , 2017, J. Frankl. Inst..

[10]  Li-Juan Liu,et al.  Stabilization for linear uncertain systems with switched time-varying delays , 2016, Neurocomputing.

[11]  Lin Sun,et al.  Input-output finite-time stability of time-varying linear singular systems , 2011, Proceedings of the 30th Chinese Control Conference.

[12]  Tadeusz Kaczorek,et al.  Selected Problems of Fractional Systems Theory , 2011 .

[13]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[14]  Francesco Amato,et al.  Input-output finite time stabilization of linear systems , 2010, Autom..

[15]  Raghib Abu-Saris,et al.  On the asymptotic stability of linear system of fractional-order difference equations , 2013 .

[16]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[17]  Mohammed Chadli,et al.  A novel approach of admissibility for singular linear continuous-time fractional-order systems , 2017 .

[18]  Jian-an Fang,et al.  Studying on the stability of fractional-order nonlinear system , 2012 .

[19]  I. Podlubny.  Fractional differential equations , 1998 .

[20]  司 苏亮.  A Refinement of Gronwall-Bellman Inequality , 2016 .

[21]  Yue-E Wang,et al.  Finite-time stability and finite-time boundedness of fractional order linear systems , 2016, Neurocomputing.

[22]  Yue-E Wang,et al.  Input–output finite time stability of fractional order linear systems with 0 < α < 1 , 2017 .

[23]  Peng Shi,et al.  Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time , 2012, IEEE Transactions on Automatic Control.

[24]  Mohamed Darouach,et al.  Robust stabilization of uncertain descriptor fractional-order systems , 2013, Autom..

[25]  Abdellah Benzaouia,et al.  Stabilization of Continuous-Time Fractional Positive Systems by Using a Lyapunov Function , 2014, IEEE Transactions on Automatic Control.

[26]  Fei Liu,et al.  Input-output finite-time stabilization of Markovian jump systems with convex polytopic switching probabilities , 2016, J. Frankl. Inst..

[27]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[28]  S. Das.  Functional Fractional Calculus , 2011 .

[29]  Leipo Liu,et al.  Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems , 2017 .

[30]  Francesco Amato,et al.  Input–output finite-time stabilization of impulsive linear systems: Necessary and sufficient conditions , 2016 .

[31]  Wiktor Malesza.  Positive fractional variable order discrete-time systems , 2017 .

[32]  Shunan Wu,et al.  Exponential stability of descriptor systems with large delay period based on a switching method , 2014, Inf. Sci..

[33]  Leipo Liu,et al.  Global Exponential Stability and Stabilization of Fractional-Order Positive Switched Systems , 2017 .

[34]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[35]  Xudong Zhao,et al.  State-dependent switching control of switched positive fractional-order systems. , 2016, ISA transactions.