Meta-sequence-dependent \(H_\infty\) filtering for switched linear systems under persistent dwell-time constraint. (English) Zbl 1461.93516
Summary: This paper is concerned with \(H_\infty\) filtering problem for a class of discrete-time switched linear systems under persistent dwell-time (PDT) constraint. A concept of meta sequence list consisting of finite switching subsequences is presented, which can represent all admissible PDT switching sequences by concatenating the list elements. Two novel Lyapunov functions only based on the meta sequence list are constructed, which break the limitation of traditional mode dependency and quasi-time dependency. Two equivalent stability criteria are accordingly developed, and the widely-used nonconvex stability conditions for PDT switched linear systems are proved to be sufficient to them. Moreover, the presented convex stability criterion is further extended to \(l_2\)-gain computation and \(H_\infty\) filter design. The designed meta-sequence-dependent (MSD) filter can guarantee that the filtering error system is globally uniformly asymptotically stable with a standard \(H_\infty\) performance index, which contrasts with the indices in weighted or parameter-dependent forms, i.e., weaker noise attenuation, in the existing literatures of switched systems under average dwell-time or PDT constraints. Two examples are provided to illustrate the effectiveness of the developed results.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93B36 | \(H^\infty\)-control |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C05 | Linear systems in control theory |
Keywords:
persistent dwell-time; meta-sequence-dependent \(H_\infty\) filtering; stability and \(l_2\)-gain analysis; switched systemsReferences:
| [1] | Basin, M.; Rodriguez-Gonzalez, J., A closed-form optimal control for linear systems with equal state and input delays, Automatica, 41, 5, 915-920 (2005) · Zbl 1087.49028 |
| [2] | Basin, M.; Rodriguez-Gonzalez, J.; Martinez-Zuñiga, R., Optimal filtering for linear state delay systems, IEEE Transactions on Automatic Control, 50, 5, 684-690 (2005) · Zbl 1365.93496 |
| [3] | Basin, M.; Shi, P.; Soto, P., Central suboptimal \(H_\infty\) filtering for nonlinear polynomial systems with multiplicative noise, Journal of the Franklin Institute, 347, 9, 1740-1754 (2010) · Zbl 1202.93048 |
| [4] | Branicky, M. S., Multiple lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control, 43, 4, 475-482 (1998) · Zbl 0904.93036 |
| [5] | Briat, C., Convex lifted conditions for robust \(l_2\)-stability analysis and \(l_2\)-stabilization of linear discrete-time switched systems with minimum dwell-time constriant, Automatica, 50, 3, 976-983 (2014) · Zbl 1298.93284 |
| [6] | Briat, C., Convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode-dependent dwell-time, Systems & Control Letters, 78, 63-72 (2015) · Zbl 1320.93064 |
| [7] | Dehghan, M.; Ong, C.-J., Characterization and computation of disturbance invariant sets for constrained switched linear systems with dwell time restriction, Automatica, 48, 9, 2175-2181 (2012) · Zbl 1257.93059 |
| [8] | Dong, H.; Hou, N.; Wang, Z., Fault estimation for complex networks with randomly varying topologies and stochastic inner couplings, Automatica, 112, 1-11 (2020) · Zbl 1430.93086 |
| [9] | Dong, H.; Wang, Z.; Gao, H., Fault detection for markovian jump systems with sensor saturations and randomly varying nonlinearities, IEEE Transactions on Circuits and Systems-I: Regular Papers, 59, 10, 2354-2362 (2012) · Zbl 1468.94903 |
| [10] | Du, D.; Xu, S.; Cocquempot, V., Fault detection for nonlinear discrete-time switched systems with persistent dwell time, IEEE Transactions on Fuzzy Systems, 26, 4, 2466-2474 (2018) |
| [11] | Fei, Z.; Shi, S.; Wang, Z.; Wu, L., Quasi-time-dependent output control for discrete-time switched system with mode-dependent average dwell time, IEEE Transactions on Automatic Control, 63, 8, 2647-2653 (2018) · Zbl 1423.93229 |
| [12] | Gao, H.; Chen, T.; Lam, J., A new delay system approach to network-based control, Automatica, 44, 1, 39-52 (2008) · Zbl 1138.93375 |
| [13] | Gao, H.; Meng, X.; Chen, T., Stabilization of networked control systems with a new delay characterization, IEEE Transactions on Automatic Control, 53, 9, 2142-2148 (2008) · Zbl 1367.93696 |
| [14] | Geromel, J.; Colaneri, P., Stability and stabilization of continuous-time switched linear systems, SIAM Journal on Control and Optimization, 45, 5, 1915-1930 (2006) · Zbl 1130.34030 |
| [15] | Geromel, J.; Colaneri, P., Stability and stabilization of discrete time switched systems, International Journal of Control, 79, 7, 719-728 (2006) · Zbl 1330.93190 |
| [16] | Han, T. T.; Ge, S. S.; Lee, T. H., Persistent dwell-time switched nonlinear systems: Variation paradigm and gauge design, IEEE Transactions on Automatic Control, 55, 2, 321-337 (2010) · Zbl 1368.93626 |
| [17] | He, Y.; Wu, M.; Liu, G.; She, J., Output feedback stabilization for a discrete-time system with a time-varying delay, IEEE Transactions on Automatic Control, 53, 10, 2372-2377 (2008) · Zbl 1367.93507 |
| [18] | He, Y.; Wu, M.; She, J.; Liu, G., Parameter-dependent lyapunov functional for stability of time-delay systems with polytopic-type uncertainties, IEEE Transactions on Automatic Control, 49, 5, 828-832 (2004) · Zbl 1365.93368 |
| [19] | Hernandez-Vargas, E.; Colaneri, P.; Middleton, R.; Blanchini, F., Discrete-time control for switched positive systems with application to mitigating viral escape, International Journal of Robust and Nonlinear Control, 21, 10, 1093-1111 (2011) · Zbl 1225.93072 |
| [20] | Hespanha, J. P., Root-mean-square gains of switched linear systems, IEEE Transactions on Automatic Control, 48, 11, 2040-2045 (2003) · Zbl 1364.93213 |
| [21] | Hespenha, J. P., Uniform stability of switched linear systems: Extensions of lasalle’s invariance principle, IEEE Transactions on Automatic Control, 49, 4, 470-482 (2004) · Zbl 1365.93348 |
| [22] | Hetel, L.; Daafouz, J.; Iung, C., Equivalence between the Lyapunov-Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems, Nonlinear Analysis. Hybrid Systems, 2, 3, 697-705 (2008) · Zbl 1215.93132 |
| [23] | Hu, J.; Wang, Z.; Gao, H., Joint state and fault estimation for time-varying nonlinear systems with randomly occurring faults and sensor saturations, Automatica, 97, 150-160 (2018) · Zbl 1406.93322 |
| [24] | Karimi, H. R., Robust delay-dependent \(H_\infty\) control of uncertain time-delay systems with mixed neutral, discrete, and distributed time-delays and markovian switching parameters, IEEE Transactions on Circuits and Systems-I: Regular Papers, 58, 8, 1910-1923 (2011) · Zbl 1468.93087 |
| [25] | Karimi, H. R.; Zapateiro, M.; Luo, N., A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations, Journal of the Franklin Institute, 347, 6, 957-973 (2010) · Zbl 1201.93033 |
| [26] | Lee, T. C.; Jiang, Z. P., Uniform asymptotic stability of nonlinear switched systems with an application to mobile robots, IEEE Transactions on Automatic Control, 53, 5, 1235-1252 (2008) · Zbl 1367.93399 |
| [27] | Liberzon, D., Switching in systems and control (2003), Birkhäuser: Birkhäuser Berlin, Germany · Zbl 1036.93001 |
| [28] | Liberzon, D.; Morse, A. S., Basic problems in stability and design of swtiched systems, IEEE Control Systems Magazine, 19, 5, 59-70 (1999) · Zbl 1384.93064 |
| [29] | Lu, B.; Wu, F., Switching LPV control designs using multiple parameter dependent Lyapunov functions, Automatica, 40, 11, 1973-1980 (2004) · Zbl 1133.93370 |
| [30] | Morse, A. S., Supervisory control of families of linear set-point controllers-Part 1: Exact matching, IEEE Transactions on Automatic Control, 41, 10, 1413-1431 (1996) · Zbl 0872.93009 |
| [31] | Palhares, R. M.; de Souza, C. E.; Peres, P. L.D., Robust \(H_\infty\) filtering for uncertain discrete-time state-delayed systems, IEEE Transactions on Signal Processing, 49, 8, 1696-1703 (2001) · Zbl 1369.93641 |
| [32] | Palhares, R. M.; Peres, P. L.D., Robust filtering with guaranteed energy-to-peak performance-an lmi approach, Automatica, 36, 6, 851-858 (2000) · Zbl 0953.93067 |
| [33] | Qin, J.; Gao, H.; Zheng, W., Second-order consensus for multi-agent systems with switching topology and communication delay, Systems & Control Letters, 60, 6, 390-397 (2011) · Zbl 1225.93020 |
| [34] | Qin, J.; Yu, C.; Hirche, S., Stationary consensus of asynchronous discrete-time second-order multi-agent systems under switching topogoly, IEEE Transactions on Industrial Informatics, 8, 4, 986-994 (2012) |
| [35] | Shen, H.; Huang, Z.; Cao, J.; Park, J. H., Exponential \(H_\infty\) filtering for continuous-time switched neural networks under persistent dwell-time switching regularity, IEEE Transactions Cybernetics, 50, 6, 2440-2449 (2020) |
| [36] | Shi, S.; Fei, Z.; Shi, P.; Ahn, C. K., Asynchronous filtering for discrete-time switched T-S fuzzy systems, IEEE Transactions on Fuzzy Systems, 28, 8, 1531-1541 (2020) |
| [37] | Shi, S.; Fei, Z.; Wang, T.; Xu, Y., Filtering for switched T-S fuzzy systems with persistent dwell time, IEEE Transactions Cybernetics, 49, 5, 1923-1931 (2019) |
| [38] | Shi, P.; Su, X.; Li, F., Dissipativity-based filtering for fuzzy switched systems with stochastic perturbation, IEEE Transactions on Automatic Control, 61, 6, 1694-1699 (2016) · Zbl 1359.93493 |
| [39] | Shi, Y.; Yu, B., Output feedback stabilization of networked control systems with random delays modeled by markov chains, IEEE Transactions on Automatic Control, 54, 7, 1668-1674 (2009) · Zbl 1367.93538 |
| [40] | Shi, P.; Zhang, Y.; Chadli, M.; Agarwal, R. K., Mixed \(H_\infty\) and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays, IEEE Transactions on Neural Networks and Learning Systems, 27, 4, 903-909 (2016) |
| [41] | Sun, X.; Zhao, J.; Hill, D. J., Stability and \(l_2\)-gain analysis for switched delay systems: A delay-dependent method, Automatica, 42, 10, 1769-1774 (2006) · Zbl 1114.93086 |
| [42] | Xiang, W.; Lam, J.; Shen, J., Stability analysis and \(L_1\)-gain characterization for switched positive systems under dwell-time constraint, Automatica, 85, 1-8 (2017) · Zbl 1375.93108 |
| [43] | Xiang, W.; Tran, H.-D.; Johnson, T. T., Robust exponential stability and disturbance attenuation for discrete-time switched systems under arbitrary switching, IEEE Transactions on Automatic Control, 63, 5, 1450-1456 (2018) · Zbl 1395.93502 |
| [44] | Xiang, W.; Tran, H.-D.; Johnson, T. T., Nonconservative lifted convex conditions for stability of discrete-time switched systems under minimum dwell-time constraint, IEEE Transactions on Automatic Control, 64, 8, 3407-3414 (2019) · Zbl 1482.93293 |
| [45] | Xiang, W.; Xiao, J., Stabilization of switched continuous-time systems with all modes unstable via dwell time switching, Automatica, 50, 3, 940-945 (2014) · Zbl 1298.93283 |
| [46] | Xu, S.; Chen, T.; Lam, J., Robust \(H_\infty\) filtering for uncertain markovian jump systems with mode-dependent time delays, IEEE Transactions on Automatic Control, 48, 5, 900-907 (2003) · Zbl 1364.93816 |
| [47] | Xu, S.; Lam, J.; Chen, T.; Zou, Y., A delay-dependent approach to robust \(H_\infty\) filtering for uncertain distributed delay systems, IEEE Transactions on Signal Processing, 53, 10, 3764-3772 (2005) · Zbl 1370.93109 |
| [48] | Zhai, G.; Hu, B.; Yasuda, K.; Michel, A. N., Disturbance attenuation properties of time-controlled switched systems, Journal of the Franklin Institute, 338, 7, 765-779 (2001) · Zbl 1022.93017 |
| [49] | Zhang, L.; Cui, N.; Liu, M.; Zhao, Y., Asynchronous filtering of discrete-time switched linear systems with average dwell time, IEEE Transactions on Circuits and Systems-I: Regular Papers, 58, 5, 1109-1118 (2011) · Zbl 1468.93072 |
| [50] | Zhang, L.; Shi, P., Stability, \( l_2\)-gain and asynchronous \(H_\infty\) control of discrete-time switched systems with average dwell time, IEEE Transactions on Automatic Control, 54, 9, 2193-2200 (2009) |
| [51] | Zhang, L.; Zhuang, S.; Shi, P., Non-weighted quasi-time-dependent \(H_\infty\) filtering for switched linear systems with persistent dwell-time, Automatica, 54, 201-209 (2015) · Zbl 1318.93094 |
| [52] | Zhao, J.; Hill, D. J., On stability, \( L_2\)-gain and \(H_\infty\) control for switched systems, Automatica, 44, 5, 1220-1232 (2008) · Zbl 1283.93147 |
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