Periodic event-based asynchronous filtering of switched systems. (English) Zbl 1423.93385
Summary: This paper provides a periodic event-based asynchronous \(\mathcal{H}_\infty\) filter design for switched systems subject to limited communication resources. The governing equations for the physical system are combined with those of the proposed event-based asynchronous filter and the resulting equations are formulated as a switched filtering error system with time-varying delay. For the achieved switched delay filtering error system, sufficient conditions in terms of linear matrix inequalities are obtained to achieve exponential stability and a prescribed \(\mathcal{H}_\infty\) disturbance attenuation level. Tools and techniques from delay-dependent Lyapunov theory, free-weighting matrices, and average dwell time for switched systems are used to obtain the main results. Further, a synthesis procedure for the filter gains, the event-triggering condition parameters, and a lower bound on the average dwell time of the switching signal is provided. A numerical example on a switched RLC circuit is finally provided to evaluate the proposed design and 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) |
| 93C65 | Discrete event control/observation systems |
Keywords:
switched systems; event-based asynchronous filtering; \(\mathcal{H}_\infty\) disturbance attenuation level; event-triggering condition parametersReferences:
| [1] | Abdelrahim, M.; Postoyan, R.; Daafouz, J.; Nešić, D.; Heemels, M., Co-design of output feedback laws and event-triggering conditions for the \(L_2\)-stabilization of linear systems, Automatica, 87, 337-344 (2018) · Zbl 1378.93080 |
| [2] | Cardim, R.; Teixeira, M. C.; Assuncao, E.; Covacic, M. R., Variable-structure control design of switched systems with an application to a DC-DC power converter, IEEE Trans. Ind. Electron., 56, 9, 3505-3513 (2009) |
| [3] | Donkers, M.; Heemels, W.; Van de Wouw, N.; Hetel, L., Stability analysis of networked control systems using a switched linear systems approach, IEEE Trans. Autom. Control, 56, 9, 2101-2115 (2011) · Zbl 1368.93465 |
| [4] | Duan, C.; Wu, F., Analysis and control of switched linear systems via dwell-time min-switching, Syst. Control Lett., 70, 8-16 (2014) · Zbl 1290.93139 |
| [5] | He, H.; Gao, X.; Qi, W., Distributed event-triggered sliding mode control of switched systems, J. Frankl. Inst. (2018) |
| [6] | Hu, L.; Wang, Z.; Han, Q.-L.; Liu, X., Event-based input and state estimation for linear discrete time-varying systems, Int. J. Control, 91, 1, 101-113 (2018) · Zbl 1390.93758 |
| [7] | Kalman, R. E., A new approach to linear filtering and prediction problems, Trans. ASME-J. Basic Eng., 82, 1, 35-45 (1960) |
| [8] | Khashooei, B. A.; Antunes, D.; Heemels, W., Output-based event-triggered control with performance guarantees, IEEE Trans. Autom. Control (2017) · Zbl 1370.93313 |
| [9] | Li, L.; Wang, X.; Lemmon, M. D., Efficiently attentive event-triggered systems with limited bandwidth, IEEE Trans. Autom. Control, 62, 3, 1491-1497 (2017) · Zbl 1366.93340 |
| [10] | Li, T.-F.; Fu, J., Event-triggered control of switched linear systems, J. Frankl. Inst. (2017) · Zbl 1373.93216 |
| [11] | Lian, J.; Li, C.; Xia, B., Sampled-data control of switched linear systems with application to an F-18 aircraft, IEEE Trans. Ind. Electron., 64, 2, 1332-1340 (2017) |
| [12] | Lian, J.; Mu, C.; Shi, P., Asynchronous \(H_∞\) filtering for switched stochastic systems with time-varying delay, Inf. Sci., 224, 200-212 (2013) · Zbl 1293.93268 |
| [13] | Liberzon, D., Switching in Systems and Control (2012), Springer Science & Business Media |
| [14] | Liu, J.; Wei, L.; Tian, E.; Fei, S.; Cao, J., \(H_∞\) filtering for networked systems with hybrid-triggered communication mechanism and stochastic cyber attacks, J. Frankl. Inst., 354, 18, 8490-8512 (2017) · Zbl 1380.93254 |
| [15] | Liu, Y.; Guo, B.-Z.; Park, J. H.; Lee, S., Event-based reliable dissipative filtering for T-S fuzzy systems with asynchronous constraints, IEEE Trans. Fuzzy Syst. (2017) |
| [16] | Ma, G.; Liu, X.; Qin, L.; Wu, G., Finite-time event-triggered \(H_∞\) control for switched systems with time-varying delay, Neurocomputing, 207, 828-842 (2016) |
| [17] | Mahmoud, M. S.; Shi, P., Asynchronous \(H_∞\) filtering of discrete-time switched systems, Signal Process., 92, 10, 2356-2364 (2012) |
| [18] | Malloci, I.; Lin, Z.; Yan, G., Stability of interconnected impulsive switched systems subject to state dimension variation, Nonlinear Anal. Hybrid Syst., 6, 4, 960-971 (2012) · Zbl 1269.93098 |
| [19] | Meng, X.; Chen, T., Event triggered robust filter design for discrete-time systems, IET Control Theory Appl., 8, 2, 104-113 (2014) · Zbl 1286.93059 |
| [20] | Niu, B.; Zhao, X.; Fan, X.; Cheng, Y., A new control method for state-constrained nonlinear switched systems with application to chemical process, Int. J. Control, 88, 9, 1693-1701 (2015) · Zbl 1337.93040 |
| [21] | Qi, Y.; Zeng, P.; Bao, W.; Feng, Z., Event-triggered robust \(H_∞\) control for uncertain switched linear systems, Int. J. Syst. Sci., 48, 15, 3172-3185 (2017) · Zbl 1386.93111 |
| [22] | Ren, H.; Zong, G.; Ahn, C. K., Event-triggered finite-time resilient control for switched systems: an observer-based approach and its applications to a boost converter circuit system model, Nonlinear Dyn., 94, 4, 2409-2421 (2018) · Zbl 1422.93145 |
| [23] | Ren, H.; Zong, G.; Karimi, H. R., Asynchronous finite-time filtering of networked switched systems and its application: an event-driven method, IEEE Trans. Circuits Syst. I Regul. Pap., 66, 1, 391-402 (2019) · Zbl 1468.93156 |
| [24] | Shen, H.; Park, J. H.; Zhang, L.; Wu, Z.-G., Robust extended dissipative control for sampled-data Markov jump systems, Int. J. Control, 87, 8, 1549-1564 (2014) · Zbl 1317.93171 |
| [25] | Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Trans. Autom. Control, 52, 9, 1680-1685 (2007) · Zbl 1366.90104 |
| [26] | Tanwani, A.; Prieur, C.; Fiacchini, M., Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization, Syst. Control Lett., 94, 46-56 (2016) · Zbl 1344.93083 |
| [27] | Viel, C.; Bertrand, S.; Michel, K.; Helene, P.-L., New state estimators and communication protocol for distributed event-triggered consensus of linear multi-agent systems with bounded perturbations, IET Control Theory Appl. (2017) |
| [28] | Vu, L.; Morgansen, K. A., Stability of time-delay feedback switched linear systems, IEEE Trans. Autom. Control, 55, 10, 2385-2390 (2010) · Zbl 1368.93573 |
| [29] | Wang, B.; Zhang, H.; Wang, G.; Dang, C., Asynchronous \(H_∞\) filtering for linear switched systems with average dwell time, Int. J. Syst. Sci., 47, 12, 2783-2791 (2016) · Zbl 1347.93258 |
| [30] | Wang, Y.-E.; Karimi, H. R.; Wu, D., Construction of hybrid interval observers for switched linear systems, Inf. Sci., 454-455, 242-254 (2018) · Zbl 1440.93114 |
| [31] | Wu, L.; Gao, Y.; Liu, J.; Li, H., Event-triggered sliding mode control of stochastic systems via output feedback, Automatica, 82, 79-92 (2017) · Zbl 1376.93030 |
| [32] | Wu, L.; Qi, T.; Feng, Z., Average dwell time approach to \(L_2-L_\infty\) control of switched delay systems via dynamic output feedback, IET Control Theory Appl., 3, 10, 1425-1436 (2009) |
| [33] | Xiao, X.; Zhou, L.; Lu, G., Event-triggered \(H_∞\) filtering of continuous-time switched linear systems, Signal Process., 141, 343-349 (2017) |
| [34] | Yin, X.; Yue, D.; Hu, S.; Peng, C.; Xue, Y., Model-based event-triggered predictive control for networked systems with data dropout, SIAM J. Control Optim., 54, 2, 567-586 (2016) · Zbl 1331.93149 |
| [35] | Zhang, D.; Xu, Z.; Karimi, H. R.; Wang, Q., Distributed filtering for switched linear systems with sensor networks in presence of packet dropouts and quantization, IEEE Trans. Circuits Syst. I Regular Pap., 64, 10, 2783-2796 (2017) |
| [36] | Zhang, J.; Feng, G., Event-driven observer-based output feedback control for linear systems, Automatica, 50, 7, 1852-1859 (2014) · Zbl 1296.93117 |
| [37] | Zhang, M.; Shi, P.; Liu, Z.; Ma, L.; Su, H., \(H_∞\) filtering for discrete-time switched fuzzy systems with randomly occurring time-varying delay and packet dropouts, Signal Process., 143, 320-327 (2018) |
| [38] | Zhang, M.; Shi, P.; Liu, Z.; Su, H.; Ma, L., Fuzzy model-based asynchronous \(H_∞\) filter design of discrete-time Markov jump systems, J. Frankl. Inst., 354, 18, 8444-8460 (2017) · Zbl 1380.93263 |
| [39] | Zou, Y.; Su, X.; Niu, Y., Mixed time/event-triggered distributed predictive control over wired-wireless networks, J. Frankl. Inst., 354, 9, 3724-3743 (2017) · Zbl 1367.93048 |
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.
