Resilient dynamic output feedback control for discrete-time descriptor switching Markov jump systems and its applications. (English) Zbl 1398.93130
Summary: This paper investigates the resilient dynamic output feedback (DOF) control problem for discrete-time descriptor switching Markov jump systems for the first time, where the time-varying transition probabilities are described by a piecewise-constant matrix and a high-level signal subject to average dwell time switching. The controllers to be designed can tolerate additive gain perturbations. Firstly, by constructing a stochastic Lyapunov functional and using an average dwell time method, a sufficient condition is given such that the resultant closed-loop systems are stochastically admissible and have a \(H_{\infty }\) noise attenuation performance. Then, based on the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition is presented such that the resultant closed-loop systems are stochastically admissible with a \(H_{\infty }\) noise attenuation performance. When the uncertain parameters exist not only in plant matrices but also in controller gain matrices, the resilient DOF controller is developed in terms of LMIs, which can be of full order or reduced order. Compared with the previous ones, the proposed design methods do not impose extra constraints on system matrices or slack variables, which show less conservatism. Finally, numerical examples are given to illustrate the superiority and applicability of the new obtained methods.
MSC:
| 93B52 | Feedback control |
| 93C55 | Discrete-time control/observation systems |
| 93E15 | Stochastic stability in control theory |
Keywords:
DOF control; resilient controllers; discrete-time descriptor Markov jump systems; average dwell time (ADT)References:
| [1] | Costa, O.L.V., Fragoso, M.D., Marques, R.P.: Discrete-time Markovian jump linear systems. Springer, London (2005) · Zbl 1081.93001 · doi:10.1007/b138575 |
| [2] | Kim, SH, Control synthesis of Markovian jump fuzzy systems based on a relaxation scheme for incomplete transition probability descriptions, Nonlinear Dyn., 78, 691-701, (2014) · Zbl 1314.93053 · doi:10.1007/s11071-014-1469-z |
| [3] | Geromel, JC; Gonçalves, APC; Fioravanti, AR, Dynamic output feedback control of discrete-time Markov jump linear systems through linear matrix inequalities, SIAM J. Control Optim., 48, 573-593, (2009) · Zbl 1194.93070 · doi:10.1137/080715494 |
| [4] | Shen, M; Ye, D; Fei, S, Robust \(H_∞ \) static output control of discrete Markov jump linear systems with norm bounded uncertainties, IET Control Theory Appl., 8, 1449-1455, (2014) · doi:10.1049/iet-cta.2013.1123 |
| [5] | Morais, CF; Braga, MF; Oliveira, RCLF; Peres, PLD, Reduced-order dynamic output feedback control of uncertain discrete-time Markov jump linear systems, Int. J. Control, 90, 2368-2383, (2017) · Zbl 1380.93233 · doi:10.1080/00207179.2016.1245871 |
| [6] | Zhang, LX; Lam, J, Necessary and sufficient conditions for analysis and synthesis of Markov jump linear systems with incomplete transition descriptions, IEEE Trans. Autom. Control, 55, 1695-1701, (2010) · Zbl 1368.93782 · doi:10.1109/TAC.2010.2046607 |
| [7] | Fioravanti, AR; Gonçalves, APC; Geromel, JC, Discrete-time \(H_∞ \) output feedback for Markov jump systems with uncertain transition probabilities, Int. J. Robust Nonlinear Control, 23, 894-902, (2013) · Zbl 1270.93117 · doi:10.1002/rnc.2807 |
| [8] | Revathi, V; Balasubramaniam, P; Park, JH; Lee, TH, \(H_∞ \) filtering for sample data systems with stochastic sampling and Markovian jumping parameters, Nonlinear Dyn., 78, 813-830, (2014) · Zbl 1331.93058 · doi:10.1007/s11071-014-1479-x |
| [9] | Aberkane, S, Stochastic stabilization of a class of nonhomogeneous Markovian jump linear systems, Syst. Control Lett., 60, 156-160, (2011) · Zbl 1210.93078 · doi:10.1016/j.sysconle.2010.11.001 |
| [10] | Yin, Y; Shi, P; Liu, F; Teo, K, Filtering for discrete-time nonhomogeneous Markov jump systems with uncertainties, Inf. Sci., 259, 118-127, (2014) · Zbl 1333.60078 · doi:10.1016/j.ins.2013.08.058 |
| [11] | Li, Z; Park, JH; Wu, ZG, Synchronization of complex networks with nonhomogeneous Markov jump topology, Nonlinear Dyn., 74, 65-75, (2013) · Zbl 1281.34088 · doi:10.1007/s11071-013-0949-x |
| [12] | Shi, Y; Yu, B, Robust mixed \(H_{2}/H_{∞ }\) control of networked control systems with random time delays in both forward and backward communication links, Automatica, 47, 754-760, (2011) · Zbl 1215.93045 · doi:10.1016/j.automatica.2011.01.022 |
| [13] | Zhang, L, \(H_∞ \) estimation for piecewise homogeneous Markov jump linear systems, Automatica, 45, 2570-2576, (2009) · Zbl 1180.93100 · doi:10.1016/j.automatica.2009.07.004 |
| [14] | Zhang, Y; Ou, Y; Wu, X; Zhou, Y, Resilient dissipative dynamic output feedback control for uncertain Markov jump lur’e systems with time-varying delays, Nonlinear Anal Hybrid Syst., 24, 13-27, (2017) · Zbl 1377.93065 · doi:10.1016/j.nahs.2016.11.002 |
| [15] | Chen, L; Leng, Y; Guo, H; Shi, P; Zhang, L, \(H_{∞ }\) control of a class of discrete-time Markov jump linear systems with piecewise-constant TPs subject to average Dwell time switching, J. Frankl. Inst., 349, 1989-2003, (2012) · Zbl 1300.93152 · doi:10.1016/j.jfranklin.2012.04.004 |
| [16] | Zhong, Q; Cheng, J; Zhao, Y; Ma, J; Huang, B, Finite-time filtering for a class of discrete-time Markovian jump systems with switching transition probabilities subject to average Dwell time switching, Appl. Math. Comput., 225, 278-294, (2013) · Zbl 1334.93173 |
| [17] | Cheng, J; Zhu, H; Zhong, S; Zhong, Q; Zhang, Y; Li, Y, Finite-time \(H_{∞ }\) control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average Dwell time switching, Int. J. Syst. Sci., 46, 1080-1093, (2015) · Zbl 1312.93109 · doi:10.1080/00207721.2013.808716 |
| [18] | Cheng, J; Zhu, H; Zhong, S; Zhong, Q; Zeng, Y, Finite-time \(H_{∞ }\) estimation for discrete-time Markov jump systems with time-varying transition probabilities subject to average Dwell time switching, Commun. Nonlinear Sci. Numer. Simul., 20, 571-582, (2015) · Zbl 1303.93183 · doi:10.1016/j.cnsns.2014.06.006 |
| [19] | Bolzern, P; Colaneri, P; DeNicolao, G, Markov jump linear systems with switching transition rates: means quare stability with Dwell-time, Automatica, 46, 1081-1088, (2010) · Zbl 1192.93119 · doi:10.1016/j.automatica.2010.03.007 |
| [20] | Bolzern, P; Colaneri, P; DeNicolao, G, Almost sure stability of Markov jump linear systems with deterministic switching, IEEE Trans. Autom. Control, 58, 209-214, (2013) · Zbl 1369.93688 · doi:10.1109/TAC.2012.2203049 |
| [21] | Hou, L; Zong, G; Zheng, W; Wu, Y, Exponential \(l_{2}-l_{∞ }\) control for discrete-time switching Markov jump linear systems, Circuits Syst. Signal Process., 32, 2745-2759, (2013) · doi:10.1007/s00034-013-9588-1 |
| [22] | Wen, J; Peng, L; Nguang, S, Finite-time analysis and design for discrete-time switching dynamics Markovian jump linear systems with time-varying delay, IET Control Theory Appl., 8, 1972-1985, (2014) · doi:10.1049/iet-cta.2014.0622 |
| [23] | Wen, J; Peng, L; Nguang, S, Stochastic finite-time boundedness on switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities, Inf. Sci., 334-335, 65-82, (2016) · Zbl 1396.93113 · doi:10.1016/j.ins.2015.11.035 |
| [24] | Ali, MS; Saravanan, S; Cao, JD, Finite-time boundedness, \(L_{2}\)-gain analysis and control of Markovian jump switched neural networks with additive time-varying delays, Nonlinear Anal. Hybrid Syst., 23, 27-43, (2017) · Zbl 1351.93162 · doi:10.1016/j.nahs.2016.06.004 |
| [25] | Dai, L.: Singular Control Systems. Springer, New York (1989) · Zbl 0669.93034 · doi:10.1007/BFb0002475 |
| [26] | Xu, S., Lam, J.: Robust Control and Filtering of Singular Systems. Springer, Berlin (2006) · Zbl 1114.93005 |
| [27] | Zhu S.Q., Li Z., Cheng Z.L.: Delay-dependent robust resilient \(H_∞ \) control for uncertain singular time-delay systems. In: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, pp. 12-15 (2005) |
| [28] | Lam, J; Shu, Z; Xu, S; Boukas, EK, Robust control of descriptor discrete-time Markovian jump systems, Int. J. Control, 80, 374-385, (2007) · Zbl 1120.93057 · doi:10.1080/00207170600999322 |
| [29] | Xia, Y; Zhang, J; Boukas, EK, Control for discrete singular hybrid systems, Automatica, 44, 2635-2641, (2008) · Zbl 1155.93359 · doi:10.1016/j.automatica.2008.02.027 |
| [30] | Ma, S; Boukas, EK, Stability and robust stabilisation for uncertain discrete stochastic hybrid singular systems with time delay, IET Control Theory Appl., 3, 1217-1225, (2009) · doi:10.1049/iet-cta.2008.0313 |
| [31] | Ma, S; Boukas, EK, Robust \(H_{∞ }\) filtering for uncertain discrete Markov jump singular systems with mode-dependent time delay, IET Control Theory Appl., 3, 351-361, (2009) · doi:10.1049/iet-cta:20080091 |
| [32] | Song, S; Ma, S; Zhang, C, Stability and robust stabilisation for a class of nonlinear uncertain discrete-time singular Markov jump systems, IET Control Theory Appl., 6, 2518-2527, (2012) · doi:10.1049/iet-cta.2012.0479 |
| [33] | Wu, ZG; Su, HY; Chu, J, Output feedback stabilization for discrete singular systems with random abrupt changes, Int. J. Robust Nonlinear Control, 20, 1945-1957, (2010) · Zbl 1202.93168 · doi:10.1002/rnc.1560 |
| [34] | Chen, J; Lin, C; Chen, B; Wang, QG, Output feedback control for singular Markovian jump systems with uncertain transition rates, IET Control Theory Appl., 10, 2142-2147, (2016) · doi:10.1049/iet-cta.2016.0548 |
| [35] | Liu, Y; Yang, R; Lu, JQ, Admissibility and static output-feedback stabilization of singular Markovian jump systems with defective statistics of modes transitions, Int. J. Robust Nonlinear Control, 25, 588-609, (2015) · Zbl 1312.93084 · doi:10.1002/rnc.3108 |
| [36] | Wu, Z; Park, J; Su, H; Chu, J, Stochastic stability analysis for discrete-time singular Markov jump systems with time-varying delay and piecewise-constant transition probabilities, J. Frankl. Inst., 349, 2889-2902, (2012) · Zbl 1264.93267 · doi:10.1016/j.jfranklin.2012.08.012 |
| [37] | Zhang, Q., Li, J., Song, Z.: Sliding mode control for discrete-time descriptor Markovian jump systems with two Markov chains. Optim. Lett. (2016). https://doi.org/10.1007/s11590-016-1085-6 · Zbl 1401.60181 |
| [38] | Wang, JM; Ma, SP; Zhang, CH, Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems, Appl. Math. Comput., 279, 90-102, (2016) · Zbl 1410.93139 |
| [39] | Wang, JM; Ma, SP; Zhang, CH, Finite-time stabilization for nonlinear discrete-time singular Markov jump systems with piecewise-constant transition probabilities subject to average Dwell time, J. Frankl. Inst., 354, 2102-2124, (2017) · Zbl 1398.93360 · doi:10.1016/j.jfranklin.2017.01.014 |
| [40] | Zhou, JP; Park, JH; Shen, H, Non-fragile reduced-order dynamic output feedback \(H_∞ \) control for switched systems with average Dwell-time switching, Int. J. Control, 89, 281-296, (2016) · Zbl 1332.93115 · doi:10.1080/00207179.2015.1075175 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
