Nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems. (English) Zbl 1448.93284
Summary: This paper considers the nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems (DPISS). Firstly, the positive observer and nonfragile positive observer are designed to estimate the actual state of the underlying systems, respectively. Secondly, by using the average dwell time (ADT) approach and multiple linear co-positive Lyapunov function (MLCLF), two guaranteed cost finite-time controller are designed and sufficient conditions are obtained to guarantee the corresponding closed-loop systems are guaranteed cost finite-time stability (GCFTS). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.
MSC:
| 93D40 | Finite-time stability |
| 93B53 | Observers |
| 93C27 | Impulsive control/observation systems |
| 93C28 | Positive control/observation systems |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
Keywords:
guaranteed cost finite-time control; nonfragile positive observer design; discrete-time positive impulsive switched systems; average dwell timeReferences:
| [1] | Niu B., Wang D., Alotaibi N.D., Alsaadi F.E., Adaptive neural state-feedback tracking control of stochastic nonlinear switched systems, IEEE Transactions on Neural Networks and Learing Systems, · doi:10.1109/TNNLS.2018.2860944 |
| [2] | Niu B., Li H., Zhang Z.H., Li J., Hayat T., Alsaadi F.E., An average dwell-time method and adaptive neural-network-based dynamic surface control for stochastic interconnected nonlinear non-strict-feedback systems with dead zone, IEEE Transactions on Systems, Man, and Cybernetics: Systems, · doi:10.1109/TSMC.2018.2866519 |
| [3] | Liu X., Li S.H., Zhang K., Optimal control of switching time in switched stochastic systems with multi-switching times and different costs, International Journal of Control, · Zbl 1367.93718 · doi:10.1080/00207179.2016.1214879 |
| [4] | Liu X., Zhang K., Li S.H., Fei S.H., Wei H., Time optimisation problem for switched stochastic systems with multi-switching times, IET Control Theory and Applications, 2014, 8(16): 1732-1740 |
| [5] | Zhao X., Liu X., Yin S., Improved results on stability of continuous-time switched positive linear systems, Automatica, 2014, 50(2): 614-621 · Zbl 1364.93583 |
| [6] | Liu S., Xiang Z., Exponential L_1 output tracking control for positive switched linear systems with time-varying delays, Nonlinear Analysis: Hybrid Systems, 2014, 11: 118-128 · Zbl 1291.93272 |
| [7] | Zong G., Ren H., Hou L., Finite-time stability of interconnected impulsive switched systems, IET Control Theory and Applications, 2016, 10(6): 648-654 |
| [8] | Zhang J., Han Z., Huang J., Stabilization of discrete-time positive switched systems Circuits Syst, Signal Process, 2013, 32(3), 1129-1145 |
| [9] | Fornasini E., Valcher M.E., Stability and stabilizability criteria for discrete-time positive switched systems, IEEE Transactions on Automatic Control, 2012, 57(5): 1208-1221 · Zbl 1369.93526 |
| [10] | Rami M.A., Tadeo F., Benzaouia A., Control of constrained positive discrete systems, American Control Conference, 2007: 5851-5856 |
| [11] | Guan Z.H., Hill D.J., Shen X., On hybrid impulsive and switching systems and application to nonlinear control, IEEE Transactions on Automatic Control, 2005, 50(7): 1058-1062 · Zbl 1365.93347 |
| [12] | Xiang M., Xiang Z., Exponential stability of discrete-time switched linear positive systems with time-delay, Applied Mathematics and Computation, 2014, 230(3): 193-199 · Zbl 1410.39031 |
| [13] | Liu T., Wu B., Liu L., Wang Y.E., Asynchronously finite-time control of discrete impulsive switched positive time-delay systems, Journal of the Franklin Institute, 2015, 352(10): 4503-4514 · Zbl 1395.93349 |
| [14] | Li X., Xiang Z., Observer design of discrete-time impulsive switched nonlinear systems with time-varying delays, Applied Mathematics and Computation, 2014, 229(6): 327-339 · Zbl 1364.93096 |
| [15] | Mahmoudi A., Momeni A., Aghdam A.G., Gohari P., On observer design for a class of impulsive switched systems, 2008 American Control Conference, 2008: 11-13 |
| [16] | Rami M.A., Helmke U., Tadeo F., Positive observation problem for linear time-delay positive systems, Conference on Control and Automation, 2008, 3(1): 1-6 |
| [17] | Xiang Z., Wang R., Jiang B., Nonfragile observer for discrete-time switched nonlinear systems with time delay, Circuits Systems and Signal Processing, 2011, 30(1): 73-87 · Zbl 1205.94147 |
| [18] | Huang S., Xiang Z., Karimi H.R., Input-output finite-time stability of discrete-time impulsive switched linear systems with state delays, Circuits Systems and Signal Processing, 2014, 33(1): 141-158 |
| [19] | Yang D., Cai K.Y., Finite-time quantized guaranteed cost fuzzy control for continuous-time nonlinear systems, Expert Systems with Applications, 2010, 37(10): 6963-6967 |
| [20] | Niamsup P., Ratchagit K., Phat V.N., Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks, Neurocomputing, 2015, 160: 281-286 |
| [21] | Zhang Y.Q., Liu L., Mu X.W, Stochastic finite-time guaranteed cost control of markovian jumping singular systems, Mathematical Problems in Engineering, 2011, 2011(11): 34-35 |
| [22] | Cai K.Y., Finite-time reliable guaranteed cost fuzzy control for discrete-time nonlinear systems, International Journal of Systems Science, 2011, 42(1): 121-128 · Zbl 1209.93088 |
| [23] | Yan Z., Zhang G., Wang J., Finite-time guaranteed cost control for linear stochastic systems, 30th Chinese Control Conference, 2011: 1389-1394 |
| [24] | Liu L., Cao X., Fu Z., Song S., Guaranteed cost finite-time control of fractional-order positive switched systems, Advances in Mathematical Physics, 2017, 2017(3): 1-11 · Zbl 1401.93118 |
| [25] | Cao X., Liu L., Fu Z., Song X., Song S., Guaranteed cost finite-time control for positive switched linear systems with time-varying delays, Journal of Control Science and Engineering, 2017, 1-10 · Zbl 1400.93127 |
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