Delay-dependent \(H_\infty\) filtering of uncertain Markovian jump delay systems via delay-partitioning approach. (English) Zbl 1395.93529
Summary: In this paper, the problem of \(H_\infty\) filtering of uncertain time-delay systems with Markovian jumping parameters is considered. Firstly, by utilizing the delay-partitioning idea, an augmented mode-dependent Lyapunov functional is employed to analyze the stochastic stability and \(H_\infty\) performance of the resulting filtering error systems. It is noted that the derived performance analysis results are less conservative than the recent ones in the literature. Secondly, based on the criteria obtained, a desired filter can be constructed by introducing a given nonsingular matrix and a scalar. Numerical examples are given to illustrate the effectiveness of the proposed approach.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93E15 | Stochastic stability in control theory |
| 60J75 | Jump processes (MSC2010) |
| 93B36 | \(H^\infty\)-control |
| 93C55 | Discrete-time control/observation systems |
| 93C41 | Control/observation systems with incomplete information |
Keywords:
\(H_\infty\) filtering; uncertain Markovian jump delay systems; delay-partitioning approach; stochastic stabilityReferences:
| [1] | Boukas, E.; Liu, Z.; Liu, G., Delay-dependent robust stability and \(H_\infty\) control of jump linear systems with time-delay, Int. J. Control, 74, 329-340, (2001) · Zbl 1015.93069 |
| [2] | Capponi, A., A convex optimization approach to filtering in jump linear systems with state dependent transitions, Automatica, 46, 383-389, (2010) · Zbl 1205.93146 |
| [3] | Costa, O.; Boukas, E., Necessary and sufficient condition for robust stability and stabilizability of continuous-time linear systems with Markovian jumps, J. Optim. Theory Appl., 99, 359-379, (1998) · Zbl 0919.93082 |
| [4] | Chen, W.; Ma, Q.; Miao, G.; Zhang, Y., Stability analysis of stochastic neural networks with Markovian jump parameters using delay-partitioning approach, Neurocomputing, 103, 22-28, (2013) |
| [5] | Du, D.; Jiang, B.; Shi, P.; Zhou, S., \(H_\infty\) filtering of discrete-time switched systems with state delays via switched Lyapunov function approach, IEEE Trans. Autom. Control, 52, 1520-1525, (2007) · Zbl 1366.93652 |
| [6] | Du, B.; Lam, J.; Shu, Z.; Wang, Z., A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components, IET Control Theory Appl., 3, 383-390, (2009) |
| [7] | Fei, Z.; Gao, H.; Shi, P., New results on stabilization of Markovian jump systems with time delay, Automatica, 45, 2300-2306, (2009) · Zbl 1179.93170 |
| [8] | Gao, H.; Fei, Z.; Lam, J.; Du, B., Further results on exponential estimates of Markovian jump systems with mode-dependent time-varying delays, IEEE Trans. Autom. Control, 56, 223-229, (2011) · Zbl 1368.93679 |
| [9] | He, Y.; Wang, G.; Xie, L.; Lin, C., Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE Trans. Autom. Control, 52, 293-299, (2007) · Zbl 1366.34097 |
| [10] | Liu, H.; Ho, D.; Sun, F., Design of \(H_\infty\) filter for Markov jumping linear systems with non-accessible mode information, Automatica, 44, 2655-2660, (2008) · Zbl 1155.93432 |
| [11] | Luan, X.; Liu, F.; Shi, P., Neural-network-based finite-time \(H_\infty\) control for extended Markov jump nonlinear systems, Int. J. Adapt. Control Signal Process., 24, 554-567, (2010) · Zbl 1200.93125 |
| [12] | Li, T.; Song, A.; Fei, S.; Wang, T., Delay-derivative-dependent for delayed neural networks with unbound distribute delay, IEEE Trans. Neural Netw., 21, 1365-1371, (2010) |
| [13] | Mao, X., Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Trans. Autom. Control, 47, 1604-1612, (2002) · Zbl 1364.93685 |
| [14] | Meng, X.; Lam, J.; Du, B.; Gao, H., A delay-partitioning approach to the stability analysis of discrete-time systems, Automatica, 46, 610-614, (2010) · Zbl 1194.93131 |
| [15] | Shi, P.; Xia, Y.; Liu, G.; Rees, D., On designing of sliding-mode control for stochastic jump systems, IEEE Trans. Autom. Control, 51, 97-103, (2006) · Zbl 1366.93682 |
| [16] | Qiu, J.; Yang, H.; Shiand, P.; Xia, Y., Robust \(H_\infty\) control for class of discrete-time Markovian jump systems with time-varying delays based on delta operator, Circuits Syst. Signal Process., 27, 627-643, (2008) · Zbl 1173.93012 |
| [17] | De Souza, C.; Trofino, A.; Barbosa, K., Mode-independent \(H_\infty\) filters for Markovian jump linear systems, IEEE Trans. Autom. Control, 51, 1837-1841, (2006) · Zbl 1366.93666 |
| [18] | Shen, H.; Xu, S.; Song, X.; Chu, Y., Delay-dependent \(H_\infty\) filtering for stochastic systems with Markovian switching and mixed mode-dependent delays, Nonlinear Anal.Hybrid Syst., 4, 122-133, (2010) · Zbl 1179.93164 |
| [19] | Wang, G.; Su, C., Delay-distribution-dependent \(H_\infty\) filtering for linear systems with stochastic time-varying delays, J. Frankl. Inst., 350, 358-377, (2013) · Zbl 1278.93275 |
| [20] | Wang, G.; Zhang, Q.; Sreeram, V., Design of reduced-order \(H_\infty\) filtering for Markovian jump systems with mode-dependent time delays, Signal Process., 89, 187-196, (2009) · Zbl 1155.94337 |
| [21] | Wang, G.; Zhang, Q.; Yang, C., Exponential \(H_\infty\) filtering for singular systems with Markovian jump parameters, Int. J. Robust. Nonlinear Control, 23, 792-806, (2013) · Zbl 1273.93164 |
| [22] | Xu, S.; Chen, T.; Lam, J., Robust \(H_\infty\) filtering for uncertain Markovian jump systems with mode-dependent time delays, IEEE Trans. Autom. Control, 48, 900-908, (2003) · Zbl 1364.93816 |
| [23] | Xiong, J.; Lam, J.; Gao, H.; Ho, D., On robust stabilization of Markovian jump systems with uncertain switching probabilities, Automatica, 41, 897-903, (2005) · Zbl 1093.93026 |
| [24] | Xu, S.; Lam, J.; Mao, X., Delay-dependent \(H_\infty\) control for uncertain Markovian jump systems with time-varying delays, IEEE Trans. Circuits Syst. IRegular Pap., 54, 2070-2077, (2007) · Zbl 1374.93134 |
| [25] | Zhao, X.; Zeng, Q., Stabilization of jump linear systems with mode-dependent time varying delays, Optimal Control Appl. Methods, 32, 139-152, (2011) · Zbl 1225.93119 |
| [26] | Zhang, L.; Boukas, E., Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities, Automatica, 45, 463-468, (2009) · Zbl 1158.93414 |
| [27] | Zhang, L.; Boukas, K., Mode-dependent \(H_\infty\) filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities, Automatica, 45, 1462-1467, (2009) · Zbl 1166.93378 |
| [28] | Zhang, X.; Han, Q., A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays, Int. J. Robust. Nonlinear Control, 19, 1922-1930, (2009) · Zbl 1185.93106 |
| [29] | Zhang, Y.; He, Y.; Wu, M.; Zhang, J., Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices, Automatica, 47, 79-84, (2011) · Zbl 1209.93162 |
| [30] | X. Zhang, X. Jiang, Q. Han, An improved stability criterion of networked control systems, in: Proceedings 2010 American Control Conference, Marriott Waterfront, Baltimore, MD, USA, 30 June-02 July 2010, pp. 586-589. |
| [31] | Zhang, L.; 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 |
| [32] | Zhang, B.; Xu, S., Robust \(H_\infty\) filtering for uncertain discrete piecewise time-delay systems, Int. J. Control, 80, 636-645, (2007) · Zbl 1117.93028 |
| [33] | Zhang, J.; Xia, Y.; Shi, P., Parameter-dependent robust \(H_\infty\) filtering for uncertain discrete-time systems, Automatica, 45, 560-565, (2009) · Zbl 1158.93406 |
| [34] | Zhao, H.; Xu, S.; Zou, Y., Robust \(H_\infty\) filtering for uncertain Markovian jump systems with mode-dependent distribute delays, Int. J. Adapt. Control Signal Process., 24, 83-94, (2010) · Zbl 1185.93138 |
| [35] | Zhu, Q.; Yang, X.; Wang, H., Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances, J. Frankl. Inst., 347, 1489-1510, (2010) · Zbl 1202.93169 |
| [36] | Zhang, B.; Zheng, W.; Xu, S., On robust \(H_\infty\) filtering of uncertain Markovian jump time-delay systems, Int. J. Adapt. Control Signal Process., 26, 138-157, (2012) · Zbl 1417.93318 |
| [37] | Zhang, B.; Zheng, We.; Xu, S., Filtering of Markovian jump delay systems based on a new performance index, IEEE Trans. Circuits Syst. IRegular Pap., 60, 1250-1263, (2013) · Zbl 1468.94288 |
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