The problem of robust H∞ reliable control for a class of delta operator switched systems with time-varying delays and actuator faults under asynchronous switching is considered in this paper. Asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. Based on the average dwell time approach and delta operator theory, a state feedback controller is designed such that the closed-loop system is exponentially stable with H∞ performance in the presence of actuator faults. The obtained results are formulated in the form of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate explicitly the feasibility and effectiveness of the proposed method.
BishopBESpongMW (1998) Control of redundant manipulators using logic-based switching. Proceedings of the 36th IEEE Conference on Decision and Control, Tampa, FL, 16–18 December, 2: pp. 16–18.
2.
ChenSIstepanianRHWuJ. (2000) Comparative study on optimizing closed loop stability bounds of finite-precision controller structures with shift and delta operators. Systems & Control Letters40(3): 153–163.
3.
De PersisCDe SantisRMorseAS (2002) Nonlinear switched systems with state dependent dwell-time. Proceedings of the 41th IEEE Conference on Decision and Control, Las Vegas, NV, 10–13 December, 4: pp. 4419–4424.
4.
EbertW (2001) Optimal filtered predictive control a delta operator approach. Systems & Control Letters42(1): 69–80.
5.
El-FarraNHChristofidesPD (2004) Coordinating feedback and switching for control of spatially distributed processes. Computers and Chemical Engineering28(1–2): 111–128.
6.
GoodwinGCAgueroJCCea GarridoME. (2013) Sampling and sampled-data models: the interface between the continuous world and digital algorithms. IEEE Control Systems33(5): 34–53.
7.
HespanhaJP (2004) Uniform stability of switched linear systems: extension of LaSalle’s invariance principle. IEEE Transactions on Automatic Control49(4): 470–482.
8.
HespanhaJPLiberzonDAngeliD. (2005) Nonlinear norm-observability notions and stability of switched systems. IEEE Transactions on Automatic Control50(2): 154–168.
9.
LeeTHWuZGParkJH (2012) Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control. Applied Mathematics and Computation219(3): 1354–1366.
10.
LennartsonBTittusMEgardtB (1996) Hybrid systems in process control. IEEE Control Systems, Magazine16(5): 45–56.
11.
LiLFengJDimirovskiGM. (2009) Reliable stabilization and robust H∞ control for switched systems with faulty actuators: an average dwell time approach. Proceedings of the American Control Conference, St Louis, MO, 10–12 June, pp. 1072–1077.
12.
MiddletonRHGoodwinGC (1990) Digital Control and Estimation: a Unified Approach. Englewood Cliffs, NJ: Prentice-Hall.
13.
QiuJXiaYYangH. (2008) Robust stabilization for a class of discrete-time systems with time-varying delays via delta operators. IET Control Theory & Applications2(1): 87–93.
14.
QinCXiangZKarimiHR (2013) Robust stability and H∞ stabilization of switched systems with time-varying delays using delta operator approach. Mathematical Problems in Engineering, Volume 2013, Article ID 230576.
15.
RichardJP (2003) Time-delay systems: an overview of some recent advances and open problems. Automatica39(10): 1667–1694.
16.
SalgadoMMiddletonRHGoodwinGC (1988) Connection between continuous and discrete Riccati equation with applications to Kalman filtering. IEE Proceedings – Control Theory and Applications135(1): 28–34.
17.
SeoCJKimBK (1996) Robust and H∞ reliable control for linear systems with parameter uncertainty and actuator failure.Automatica32(3): 465–467.
18.
SohCB (1991) Robust stability of discrete-time systems using delta operators. IEEE Transactions on Automatic Control36(3): 377–380.
19.
VaraiyaPP (1993) Smart Cars on smart roads: problems of control. IEEE Transactions on Automatic Control38(2): 195–207.
20.
VijayanRPoorHVMooreJB. (1991) A Levinson-type algorithm for modeling fast sampled data. IEEE Transactions on Automatic Control36(3): 314–321.
21.
WangHLamJXuS. (2002) Robust H∞ reliable control for a class of uncertain neutral delay systems. International Journal of Systems Science33(7): 611–622.
22.
WangRXingJWangP. (2012) Non-fragile observer design for nonlinear time delay systems using delta operator. 2012 UKACC International Conference on Control, Cardiff, UK, 3–5 September, pp. 387–393.
23.
WangYBHanZJLuoZW (1997) Opening study of intelligent transportation systems. Control and Decision12(1): 403–407.
24.
WangZ (1998) Robust H∞ reliable control for linear state delayed systems with parameter uncertainty. Proceedings of the 1998 American Control Conference, Philadelphia, PA, 21–26 Jun 1998, 4: pp. 2405–2409.
25.
WuJChenSLiG. (2000) Shift and delta operator realizations for digital controllers with finite word length considerations. IEE Proceedings – Control Theory and Applications147(6): 664–672.
26.
XiangWXiaoJ (2011) H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance. Journal of the Franklin Institute348(2): 331–352.
27.
XiangWXiaoJ (2012) Discussion on ‘Stability, L2 gain and asynchronous H∞ control of discrete time switched systems with average dwell time’. IEEE Transactions on Automatic Control57(12): 3259–3261.
28.
XiangWXiaoJIqbalMN (2011) Fault detection for switched nonlinear systems under asynchronous switching. International Journal of Control84(8): 1362–1376.
29.
XiangZChenQHuW (2002) Robust H∞ control of interval systems using the delta operator. Proceedings of the 4th World Congress on Intelligent Control and Automation, Shanghai, China, 10–14 June, 3: pp. 1731–1733.
30.
XiangZSunYNChenQ (2011) Robust reliable stabilization of uncertain switched neutral systems with delayed switching. Applied Mathematics and Computation217(23): 9835–9844.
31.
XiangZWangR (2009a) Robust control for uncertain switched non-linear systems with time delay under asynchronous switching. IET Control Theory & Applications3(8): 1041–1050.
32.
XiangZWangR (2009b) Robust L∞ reliable control for uncertain nonlinear switched systems with time delay. Applied Mathematics and Computation210(1): 202–210.
33.
XiangZWangR (2010) Robust H∞ control for a class of uncertain switched systems using delta operator. Transactions of the Institute of Measurement and Control32(3): 331–344.
34.
XiangZWangRChenQ (2011) Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching. Applied Mathematics and Computation217(19): 7725–7736.
35.
XingJWangRWangP. (2012) Robust control for a class of uncertain switched time delay systems using delta operator. 12th International Conference on Control Automation Robotics & Vision, Guangzhou, China, 5–7 December, pp. 518–523.
36.
YangHXiaYQiuJ. (2010) Filtering for a class of discrete-time systems with time-delays via delta operator approach. International Journal of Systems Science41(4): 423–433.
37.
YuzJIGoodwinGC (2014) Sampled-Data Models for Linear and Nonlinear Systems. Berlin: Springer.
38.
ZhangDJYangCW (1998) Delta-operator theory for feedback control system – a survey. Control Theory & Applications15(2): 153–160.
39.
ZhangLGaoH (2010) Asynchronously switched control of switched linear systems with average dwell time. Automatica46(5): 953–958.
40.
ZhangLCuiNLiuM. (2011) Asynchronous filtering of discrete-time switched linear systems with average dwell time. IEEE Transactions on Circuits Systems58(5): 1109–1118.
41.
ZhangWBranickyMSPhillipsSM (2001) Stability of networked control systems. IEEE Control Systems, Magazine21(1): 84–99.
42.
ZhaoXShiPZhangL (2012) Asynchronously switched control of a class of slowly switched linear systems. Systems & Control Letters61(12): 1151–1156.
