Mixed \(H_\infty\) and passive filtering for a class of singular systems with interval time-varying delays. (English) Zbl 1390.93254
Summary: This paper deals with the problem of mixed \(H_\infty\) and passive filtering for a class of singular systems with interval time-varying delays. First, by combining the Wirtinger-based integral inequality with the reciprocally convex inequality, sufficient delay-range-dependent conditions are obtained in terms of strict linear matrix inequalities to ensure that the considered singular system is admissible with a mixed \(H_\infty\) and passivity performance level. Then, based on a matrix transformation technique and employing several free scalars, more flexible strict linear matrix inequality-based conditions are proposed to get the desired filter. Finally, 2 numerical examples are given to show less conservatism and the effectiveness of the results.
MSC:
| 93B35 | Sensitivity (robustness) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93B36 | \(H^\infty\)-control |
| 93D30 | Lyapunov and storage functions |
| 93C05 | Linear systems in control theory |
Keywords:
LMIs; mixed \(H_\infty\) and passive filtering; singular systems; time-varying delays; Wirtinger-based integral inequalityReferences:
| [1] | 1 Hodgson SP, Stoten DP. Passivity‐based analysis of the minimal control synthesis algorithm. {\it Int J Control}. 1996;63(1):67‐84. · Zbl 0854.93055 |
| [2] | 2 Xu S, Zheng WX, Zou Y. Passivity analysis of neural networks with time‐varying delays. {\it IEEE Trans Circuits Syst II: Express Briefs}. 2009;56(4):325‐329. |
| [3] | 3 Li H, Gao H, Shi P. New passivity analysis for neural networks with discrete and distributed delays. {\it IEEE Trans Neural Netw}. 2010;21(11):1842‐1847. |
| [4] | 4 Shen H, Xu S, Lu J, Zhou J. Passivity‐based control for uncertain stochastic jumping systems with mode‐dependent round‐trip time delays. {\it J Franklin Inst}. 2012;349(5):1665‐1680. · Zbl 1254.93148 |
| [5] | 5 Shen H, Su L, Park JH. Extended passive filtering for discrete‐time singular Markov jump systems with time‐varying delays. {\it Signal Process}. 2016;128:68‐77. |
| [6] | 6 Wu L, Zheng WX. Passivity‐based sliding mode control of uncertain singular time‐delay systems. {\it Automatica}. 2009;45(9):2120‐2127. · Zbl 1175.93065 |
| [7] | 7 Sakthivel R, Joby M, Mathiyalagan K, Santra S. Mixed urn:x-wiley:oca:media:oca2352:oca2352-math-0177 and passive control for singular Markovian jump systems with time delays. {\it J Franklin Inst}. 2015;352(10):4446‐4466. · Zbl 1395.93197 |
| [8] | 8 Shen H, Wu Z, Park JH. Reliable mixed passive and urn:x-wiley:oca:media:oca2352:oca2352-math-0178 filtering for semi‐Markov jump systems with randomly occurring uncertainties and sensor failures. {\it Int J Robust Nonlin Control}. 2015;25(17):3231‐3251. · Zbl 1338.93378 |
| [9] | 9 Shi P, Zhang Y, Chadli M, Agarwal RK. Mixed H‐infinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays. {\it IEEE Trans Neural Netw Learn Syst}. 2016;27(4):903‐909. |
| [10] | 10 Sun J, Liu G, Chen J, Rees D. Improved delay‐range‐dependent stability criteria for linear systems with time‐varying delays. {\it Automatica}. 2010;46(2):466‐470. · Zbl 1205.93139 |
| [11] | 11 Park P, Ko JW, Jeong C. Reciprocally convex approach to stability of systems with time‐varying delays. {\it Automatica}. 2011;47(1):235‐238. · Zbl 1209.93076 |
| [12] | 12 Wu Z, Shi P, Su H, Chu J. Delay‐dependent stability analysis for switched neural networks with time‐varying delay. {\it IEEE Trans Syst, Man Cybern, Part B Cybern}. 2011;41(6):1522‐1530. |
| [13] | 13 Wu Z, Shi P, Su H, Chu J. Dissipativity analysis for discrete‐time stochastic neural networks with time‐varying delays. {\it IEEE Trans Neural Netw Learn Syst}. 2013;24(3):345‐355. |
| [14] | 14 Seuret A, Gouaisbaut F. Wirtinger‐based integral inequality: application to time‐delay systems. {\it Automatica}. 2013;49(9):2860‐2866. · Zbl 1364.93740 |
| [15] | 15 Lu R, Wu H, Bai J. New delay‐dependent robust stability criteria for uncertain neutral systems with mixed delays. {\it J Franklin Inst}. 2014;351(3):1386‐1399. · Zbl 1395.93467 |
| [16] | 16 Xu S, Lam J, Zhang B, Zou Y. New insight into delay‐dependent stability of time‐delay systems. {\it Int J Robust Nonlin Control}. 2015;25(7):961‐970. · Zbl 1312.93077 |
| [17] | 17 Park PG, Lee WI, Lee SY. Auxiliary function‐based integral inequalities for quadratic functions and their applications to time‐delay systems. {\it J Franklin Inst}. 2015;352(4):1378‐1396. · Zbl 1395.93450 |
| [18] | 18 Xu Y, Lu R, Shi P, Tao J, Xie S. Robust estimation for neural networks with randomly occurring distributed delays and Markovian jump coupling. {\it IEEE Trans Neural Netw Learn Syst}. 2016. https://doi.org/10.1109/TNNLS.2016.2636325 |
| [19] | 19 Lee TH, Park JH, Xu S. Relaxed conditions for stability of time‐varying delay systems. {\it Automatica}. 2017;75:11‐15. · Zbl 1351.93122 |
| [20] | 20 Liu K, Seuret A, Xia Y. Stability analysis of systems with time‐varying delays via the second‐order Bessel‐Legendre inequality. {\it Automatica}. 2017;76:138‐142. · Zbl 1352.93079 |
| [21] | 21 Xu S, Lam J. Robust Control and Filtering of Singular Systems. Berlin: Springer; 2006. · Zbl 1114.93005 |
| [22] | 22 Boukas EK. Singular linear systems with delay: urn:x-wiley:oca:media:oca2352:oca2352-math-0179 stabilization. {\it Optim Control Appl Methods}. 2007;28(4):259‐274. |
| [23] | 23 Zhu S, Zhang C, Cheng Z, Feng J. Delay‐dependent robust stability criteria for two classes of uncertain singular time‐delay systems. {\it IEEE Trans Autom Control}. 2007;52(5):880‐885. · Zbl 1366.93478 |
| [24] | 24 Shu Z, Lam J. Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays. {\it Int J Control}. 2008;81(6):865‐882. · Zbl 1152.93462 |
| [25] | 25 Du Z, Zhang Q, Chang G. Delay‐dependent robust urn:x-wiley:oca:media:oca2352:oca2352-math-0180 control for uncertain descriptor systems with multiple state delays. {\it Optim Control Appl Methods}. 2009;31(4):375‐387. · Zbl 1204.93041 |
| [26] | 26 Haidar A, Boukas EK. Exponential stability of singular systems with multiple time‐varying delays. {\it Automatica}. 2009;45(2):539‐545. · Zbl 1158.93347 |
| [27] | 27 Wu Z, Park JH, Su H, Chu J. Dissipativity analysis for singular systems with time‐varying delays. {\it Appl Math Comput}. 2011;218(8):4605‐4613. · Zbl 1256.34062 |
| [28] | 28 Mourad K, Fernando T, Mohamed C. A partitioning approach for urn:x-wiley:oca:media:oca2352:oca2352-math-0181 control of singular time‐delay systems. {\it Optim Control Appl Methods}. 2013;34(4):472‐486. · Zbl 1302.93094 |
| [29] | 29 Wu Z, Park JH, Su H, Chu J. Reliable passive control for singular systems with time‐varying delays. {\it J Process Control}. 2013;23(8):1217‐1228. |
| [30] | 30 Chen H, Hu P. New result on exponential stability for singular systems with two interval time‐varying delays. {\it IET Control Theory Appl}. 2013;7(15):1941‐1949. |
| [31] | 31 Hien LV, Vu LH, Phat VN. Improved delay‐dependent exponential stability of singular systems with mixed interval time‐varying delays. {\it IET Control Theory Appl}. 2015;9(9):1364‐1372. |
| [32] | 32 Liu Z, Lin C, Chen B. Admissibility analysis for linear singular systems with time‐varying delays via neutral system approach. {\it ISA Trans}. 2016;61:141‐146. |
| [33] | 33 Li F, Zhang X. A delay‐dependent bounded real lemma for singular LPV systems with time‐variant delay. {\it Int J Robust Nonlin Control}. 2012;22(5):559‐574. · Zbl 1273.93088 |
| [34] | 34 Wu Z, Su H, Chu J. urn:x-wiley:oca:media:oca2352:oca2352-math-0182 filtering for singular systems with time‐varying delay. {\it Int J Robust Nonlin Control}. 2009;20(11):1269‐1284. · Zbl 1200.93133 |
| [35] | 35 Zhu X, Wang Y, Gan Y. urn:x-wiley:oca:media:oca2352:oca2352-math-0183 filtering for continuous‐time singular systems with time‐varying delay. {\it Int J Adapt Control Signal Process}. 2011;25(2):137‐154. · Zbl 1213.93057 |
| [36] | 36 Lu R, Xu Y, Xue A. urn:x-wiley:oca:media:oca2352:oca2352-math-0184 filtering for singular systems with communication delays. {\it Signal Process}. 2010;90(4):1240‐1248. · Zbl 1197.94084 |
| [37] | 37 Zhang B, Zheng WX, Xu S. Filtering of Markovian jump delay systems based on a new performance index. {\it IEEE Trans Circuits Syst I: Regular Pap}. 2013;60(5):1250‐1263. · Zbl 1468.94288 |
| [38] | 38 Zhuang G, Xu S, Zhang B, Xu H, Chu Y. Robust urn:x-wiley:oca:media:oca2352:oca2352-math-0185 deconvolution filtering for uncertain singular Markovian jump systems with time‐varying delays. {\it Int J Robust Nonlin Control}. 2016;26(12):2564‐2585. · Zbl 1346.93388 |
| [39] | 39 Du Z, Yue D, Hu S. H‐infinity stabilization for singular networked cascade control systems with state delay and disturbance. {\it IEEE Trans Ind Inform}. 2014;10(2):882‐894. |
| [40] | 40 Shi P, Wang H, Lim CC. Network‐based event‐triggered control for singular systems with quantizations. {\it IEEE Trans Ind Electron}. 2016;63(2):1230‐1238. |
| [41] | 41 Zhang W, Chen B, Chen M. Hierarchical fusion estimation for clustered asynchronous sensor networks. {\it IEEE Trans Autom Control}. 2016;61(10):3064‐3069. · Zbl 1359.93475 |
| [42] | 42 Yan H, Qian F, Zhang H, Yang F, Guo G. urn:x-wiley:oca:media:oca2352:oca2352-math-0186 fault detection for networked mechanical spring‐mass systems with incomplete information. {\it IEEE Trans Ind Electron}. 2016;63(9):5622‐5631. |
| [43] | 43 Lu R, Xu Y, Zhang R. A new design of model predictive tracking control for networked control system under random packet loss and uncertainties. {\it IEEE Trans Ind Electron}. 2016;63(11):6999‐7007. |
| [44] | 44 Zhang H, Hong Q, Yan H, Yang F, Guo G. Event‐based distributed urn:x-wiley:oca:media:oca2352:oca2352-math-0187 filtering networks of 2‐DOF quarter‐car suspension systems. {\it IEEE Trans Ind Inform}. 2017;13(1):312‐321. |
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.
