This paper considers the problem of anti-disturbance control for discrete-time Markovian jump systems with multiple disturbances. The controller is constructed via disturbance-observer-based control and l2–l∞ control. The disturbances are divided into two parts. One, in the same channel as the control inputs, is described by an exogenous system. The other is assumed to be bounded with an norm. A disturbance observer is presented to estimate and reject the first-case disturbances for discrete-time Markovian jump systems, and an l2–l∞ control scheme is used to attenuate the second-case disturbances. By using linear matrix inequalities, a solvable sufficient condition is developed. Finally, the effectiveness of the proposed control scheme is demonstrated via a numerical example.
BackJShimH (2014) Reduced-order implementation of disturbance observers for robust tracking of non-linear systems. IET Control Theory and Applications8(17): 1940–1948.
2.
BoukasEKLiuZK (2001) Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays. IEEE Transactions on Automatic Control46(12): 1918–1924.
3.
ChenW (2003) Nonlinear disturbance observer-enhanced dynamic inversion control of missiles. Journal of Guidance Control and Dynamics26(1): 161–166.
4.
ChenW (2004) Disturbance observer based control for nonlinear systems. IEEE/ASME Transactions on Mechatronics9(4): 706–710.
5.
CostaOLVFragosoMDMarquesRP (2005) Discrete-Time Markovian Jump Linear Systems. London: Springer-Verlag.
DingSHWangJDZhengWX (2015) Second-order sliding mode control for nonlinear uncertain systems bounded by positive functions. IEEE Transactions on Industrial Electronics62(9): 5899–5909.
8.
GuoLChenWH (2005) Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. International Journal of Robust and Nonlinear Control15(3): 109–125.
9.
GuoLWenXY (2011) Hierarchical anti-disturbance adaptive control for non-linear systems with composite disturbances and applications to missile systems. Transactions of the Institute of Measurement and Control33(8): 942–956.
10.
KchaouMHajjajiAEToumiA (2015) Non-fragile H∞ output feedback control design for continuous-time fuzzy systems. ISA Transactions54: 3–14.
11.
LiSSunHSunC (2012) Composite controller design for an airbreathing hypersonic vehicle. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering226(5): 651–664.
12.
LiSYangJChenWet al. (2014) Disturbance Observer-Based Control for Nonlinear Systems. Boca Raton: CRC Press.
13.
LiYSunHZongGet al. (2017a) Composite anti-disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. International Journal of Robust and Nonlinear Control27(14): 2323–2337.
14.
LiYSunHZongGet al. (2017b) Composite adaptive anti-disturbance resilient control for Markovian jump systems with partly known transition rate and multiple disturbances. International Journal of Adaptive Control and Signal Processing31(7): 1077–1097.
15.
LiuHLinX (2015) Finite-time H∞ control for a class of nonlinear system with time-varying delay. Neurocomputing14(9): 1481–1489.
16.
MarinoRTomeiP (1995) Nonlinear Control Design: Geometric, Adaptive and Robust. London: Prentice-Hall.
17.
SunHGuoL (2017) Neural network-based DOBC for a class of nonlinear systems with unmatched disturbances. IEEE Transactions on Neural Networks and Learning Systems28(2): 482–489.
18.
SunHHouLZongG (2016) Continuous finite time control for static var compensator with mismatched disturbances. Nonlinear Dynamics85(4): 2159–2169.
19.
SunHHouLZongGet al. (2017) Composite anti-disturbance attitude and vibration control for flexible spacecraft. IET Control Theory & Applications11(14): 2383–2390.
20.
SunHLiSSunC (2013) Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dynamics73(1–2): 229–244.
21.
SzpruchLHighamDJ (2010) Comparing hitting time behavior of Markov jump processes and their diffusion approximations. Multiscale Modeling & Simulation8(2): 605–621.
22.
WeiXJGuoL (2009) Composite disturbance-observer-based control and terminal sliding mode control for non-linear systems with disturbances. International Journal of Control82(6): 1082–1098.
23.
WeiXJGuoL (2010) Composite disturbance-observer-based control and H∞ control for complex continuous models. International Journal of Robust and Nonlinear Control20(1): 106–118.
24.
XieL (1996) Output feedback H∞ control of systems with parameter uncertainty. International Journal of Control63(4): 741–750.
25.
XuSLamJMaoX (2007) Delay-dependent H∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Transactions on Circuits and Systems I: Regular Papers54(9): 2070–2077.
26.
YangJLiSChenW (2012) Nonlinear disturbance observer-based control for multi-input multi-output nonlinear systems subject to mismatching condition. International Journal of Control85(8): 1071–1082.
27.
YaoXGuoL (2013) Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer. Automatica49(8): 2538–2545.
28.
YaoXGuoL (2014) Disturbance attenuation and rejection for discrete-time Markovian jump systems with lossy measurements. Information Sciences278: 673–684.
29.
YaoXZhuLGuoL (2014) Disturbance-observer-based control & H∞ control for non-linear Markovian jump singular systems with multiple disturbances. IET Control Theory & Applications8(16): 1689–1697.
30.
ZhuYZhangLBasinMV (2015) Nonstationary H∞ dynamic output feedback control for discrete-time Markov jump linear systems with actuator and sensor saturations. International Journal of Robust and Nonlinear Control10: 1002–3348.
31.
ZongGYangDHouLet al. (2013) Robust finite-time H∞ control for Markovian jump systems with partially known transition probabilities. Journal of the Franklin Institute350(6): 1562–1578.
